Trade-offs in WWII Fighter Design

[Collimatrix]

But if you try sometimes...

Fighter aircraft became much better during the Second World War.  But, apart from the development of engines, it was not a straightforward matter of monotonous improvement.  Aircraft are a series of compromises.  Improving one aspect of performance almost always compromises others.  So, for aircraft designers in World War Two, the question was not so much "what will we do to make this aircraft better?" but "what are we willing to sacrifice?"


 

To explain why, let's look at the forces acting on an aircraft:

Lift
 

Lift is the force that keeps the aircraft from becoming one with the Earth.  It is generally considered a good thing. 

 

The lift equation is L=0.5C_LRV²A where L is lift, C_L is lift coefficient (which is a measure of the effectiveness of the wing based on its shape and other factors), R is air density, V is airspeed and A is the area of the wing.

Airspeed is very important to an aircraft's ability to make lift, since the force of lift grows with the square of airspeed and in linear relation to all other factors.  This means that aircraft will have trouble producing adequate lift during takeoff and landing, since that's when they slow down the most.

 

Altitude is also a significant factor to an aircraft's ability to make lift.  The density of air decreases at an approximately linear rate with altitude above sea level:



Finally, wings work better the bigger they are.  Wing area directly relates to lift production, provided that wing shape is kept constant.

While coefficient of lift C_L contains many complex factors, one important and relatively simple factor is the angle of attack, also called AOA or alpha.  The more tilted an airfoil is relative to the airflow, the more lift it will generate.  The lift coefficient (and thus lift force, all other factors remaining equal) increases more or less linearly until the airfoil stalls:





Essentially what's going on is that the greater the AOA, the more the wing "bends" the air around the wing.  But the airflow can only become so bent before it detaches.  Once the wing is stalled it doesn't stop producing lift entirely, but it does create substantially less lift than it was just before it stalled.  

Drag
 

Drag is the force acting against the movement of any object travelling through a fluid.  Since it slows aircraft down and makes them waste fuel in overcoming it, drag is a total buzzkill and is generally considered a bad thing.

The drag equation is D=0.5C_DRV²A where D is drag, C_D is drag coefficient (which is a measure of how "draggy" a given aircraft is), R is air density, V is airspeed and A is the frontal area of the aircraft.

This equation is obviously very similar to the lift equation, and this is where designers hit the first big snag.  Lift is good, but drag is bad, but because the factors that cause these forces are so similar, most measures that will increase lift will also increase drag.  Most measures that reduce drag will also reduce lift.

Generally speaking, wing loading (the amount of wing area relative to the plane's weight) increased with newer aircraft models.  The stall speed (the slowest possible speed at which an aircraft can fly without stalling) also increased.  The massive increases in engine power alone were not sufficient to provide the increases in speed that designers wanted.  They had to deliberately sacrifice lift production in order to minimize drag.

 

World War Two saw the introduction of laminar-flow wings.  These were wings that had a cross-section (or airfoil) that generated less turbulent airflow than previous airfoil designs.  However, they also generated much less lift.  Watch a B-17 (which does not have a laminar-flow wing) and a B-24 (which does) take off.  The B-24 eats up a lot more runway before its nose pulls up.


 

There are many causes of aerodynamic drag, but lift on a WWII fighter aircraft can be broken down into two major categories.  There is induced drag, which is caused by wingtip vortices and is a byproduct of lift production, and parasitic drag which is everything else.  Induced drag is interesting in that it actually decreases with airspeed.  So for takeoff and landing it is a major consideration, but for cruising flight it is less important.

However, induced drag is also significant during combat maneuvering.  Wing with a higher aspect ratio, that is, the ratio of the wingspan to the wing chord (which is the distance from the leading edge to the trailing edge of the wing) produce less induced drag.

 

So, for the purposes of producing good cruise efficiency, reducing induced drag was not a major consideration.  For producing the best maneuvering fighter, reducing induced drag was significant.

Weight
 

Weight is the force counteracting lift.  The more weight an aircraft has, the more lift it needs to produce.  The more lift it needs to produce, the larger the wings need to be and the more drag they create.  The more weight an aircraft has, the less it can carry.  The more weight an aircraft has, the more sluggishly it accelerates.  In general, weight is a bad thing for aircraft.  But for fighters in WWII, weight wasn't entirely a bad thing.  The more weight an aircraft has relative to its drag, the faster it can dive.  Diving away to escape enemies if a fight was not going well was a useful tactic.  The P-47, which was extremely heavy, but comparatively well streamlined, could easily out-dive the FW-190A and Bf-109G/K.

In general though, designers tried every possible trick to reduce aircraft weight.  Early in the war, stressed-skin monocoque designs began to take over from the fabric-covered, built-up tube designs.


The old-style construction of the Hawker Hurricane.  It's a shit plane.

 

Stressed-skin construction of the Spitfire, with a much better strength to weight ratio.

 

But as the war dragged on, designers tried even more creative ways to reduce weight.  This went so far as reducing the weight of the rivets holding the aircraft together, stripping the aircraft of any unnecessary paint, and even removing or downgrading some of the guns.


An RAF Brewster Buffalo in the Pacific theater.  The British downgraded the .50 caliber machine guns to .303 weapons in order to reduce weight.

 

In some cases, however, older construction techniques were used at the war's end due to materials shortages or for cost reasons.  The German TA-152, for instance, used a large amount of wooden construction with steel reinforcement in the rear fuselage and tail in order to conserve aluminum.  This was not as light or as strong as aluminum, but beggars can't be choosers.

Extensive use of (now rotten) wood in the rear fuselage of the TA-152

 

Generally speaking, aircraft get heavier with each variant.  The Bf-109C of the late 1930s weighed 1,600 kg, but the Bf-109G of the second half of WWII had ballooned to over 2,200 kg.  One notable exception was the Soviet YAK-3:

 

The YAK-3, which was originally designated YAK-1M, was a demonstration of what designers could accomplish if they had the discipline to keep aircraft weight as low as possible.  Originally, it had been intended that The YAK-1 (which had somewhat mediocre performance vs. German fighters) would be improved by installing a new engine with more power.  But all of the new and more powerful engines proved to be troublesome and unreliable.  Without any immediate prospect of more engine power, the Yakovlev engineers instead improved performance by reducing weight.  The YAK-3 ended up weighing nearly 300 kg less than the YAK-1, and the difference in performance was startling.  At low altitude the YAK-3 had a tighter turn radius than anything the Luftwaffe had.  

 

Thrust

 

Thrust is the force propelling the aircraft forwards.  It is generally considered a good thing.  Thrust was one area where engineers could and did make improvements with very few other compromises.  The art of high-output piston engine design was refined during WWII to a precise science, only to be immediately rendered obsolete by the development of jet engines.

 

Piston engined aircraft convert engine horsepower into thrust airflow via a propeller.  Thrust was increased during WWII primarily by making the engines more powerful, although there were also some improvements in propeller design and efficiency.  A tertiary source of thrust was the addition of jet thrust from the exhaust of the piston engines and from Merideth Effect radiators.

 

The power output of WWII fighter engines was improved in two ways; first by making the engines larger, and second by making the engines more powerful relative to their weight.  Neither process was particularly straightforward or easy, but nonetheless drastic improvements were made from the war's beginning to the war's end.

The Pratt and Whitney Twin Wasp R-1830-1 of the late 1930s could manage about 750-800 horsepower.  By mid-war, the R-1830-43 was putting out 1200 horsepower out of the same displacement.  Careful engineering, gradual improvements, and the use of fuel with a higher and more consistent octane level allowed for this kind of improvement.

The R-1830 Twin Wasp

However, there's no replacement for displacement.  By the beginning of 1943, Japanese aircraft were being massacred with mechanical regularity by a new US Navy fighter, the F6F Hellcat, which was powered by a brand new Pratt and Whitney engine, the R-2800 Double Wasp.


The one true piston engine

As you can see from the cross-section above, the R-2800 has two banks of cylinders.  This is significant to fighter performance because even though it had 53% more engine displacement than the Twin Wasp (For US engines, the numerical designation indicated engine displacement in square inches), the Double Wasp had only about 21% more frontal area.  This meant that a fighter with the R-2800 was enjoying an increase in power that was not proportionate with the increase in drag.  Early R-2800-1 models could produce 1800 horsepower, but by war's end the best models could make 2100 horsepower.  That meant a 45% increase in horsepower relative to the frontal area of the engine.  Power to weight ratios for the latest model R-1830 and R-2800 were similar, while power to displacement improved by about 14%.

 

By war's end Pratt and Whitney had the monstrous R-4360 in production:



This gigantic engine had four rows of radially-arranged pistons.  Compared to the R-2800 it produced about 50% more power for less than 10% more frontal area.  Again, power to weight and power to displacement showed more modest improvements.  The greatest gains were from increasing thrust with very little increase in drag.  All of this was very hard for the engineers, who had to figure out how to make crankshafts and reduction gear that could handle that much power without breaking, and also how to get enough cooling air through a giant stack of cylinders.

Attempts at boosting the thrust of fighters with auxiliary power sources like rockets and ramjets were tried, but were not successful.


Yes, that is a biplane with retractable landing gear and auxiliary ramjets under the wings.  Cocaine is a hell of a drug.

A secondary source of improvement in thrust came from the development of better propellers.  Most of the improvement came just before WWII broke out, and by the time the war broke out, most aircraft had constant-speed propellers.



For optimal performance, the angle of attack of the propeller blades must be matched to the ratio of the forward speed of the aircraft to the circular velocity of the propeller tips.  To cope with the changing requirements, constant speed or variable pitch propellers were invented that could adjust the angle of attack of the propeller blades relative to the hub.



There was also improvement in using exhaust from the engine and the waste heat from the engine to increase thrust.  Fairly early on, designers learned that the enormous amount of exhaust produced by the engine could be directed backwards to generate thrust.  Exhaust stacks were designed to work as nozzles to harvest this small source of additional thrust:


The exhaust stacks of the Merlin engine in a Spitfire act like jet nozzles

A few aircraft also used the waste heat being rejected by the radiator to produce a small amount of additional thrust.  The Meredith Effect radiator on the P-51 is the best-known example:



Excess heat from the engine was radiated into the moving airstream that flowed through the radiator.  The heat would expand the air, and the radiator was designed to use this expansion and turn it into acceleration.  In essence, the radiator of the P-51 worked like a very weak ramjet.  By the most optimistic projections the additional thrust from the radiator would cancel out the drag of the radiator at maximum velocity.  So, it may not have provided net thrust, but it did still provide thrust, and every bit of thrust mattered.
 

 

For the most part, achieving specific design objectives in WWII fighters was a function of minimizing weight, maximizing lift, minimizing drag and maximizing thrust.  But doing this in a satisfactory way usually meant emphasizing certain performance goals at the expense of others.

 

Top Speed, Dive Speed and Acceleration

 

During the 1920s and 1930s, the lack of any serious air to air combat allowed a number of crank theories on fighter design to develop and flourish.  These included the turreted fighter:



The heavy fighter:



And fighters that placed far too much emphasis on turn rate at the expense of everything else:



But it quickly became clear, from combat in the Spanish Civil War, China, and early WWII, that going fast was where it was at.  In a fight between an aircraft that was fast and an aircraft that was maneuverable, the maneuverable aircraft could twist and pirouette in order to force the situation to their advantage, while the fast aircraft could just GTFO the second that the situation started to sour.  In fact, this situation would prevail until the early jet age when the massive increase in drag from supersonic flight made going faster difficult, and the development of heat-seeking missiles made it dangerous to run from a fight with jet nozzles pointed towards the enemy.

 

The top speed of an aircraft is the speed at which drag and thrust balance each other out, and the aircraft stops accelerating.  Maximizing top speed means minimizing drag and maximizing thrust.  The heavy fighters had a major, inherent disadvantage in terms of top speed.  This is because twin engined prop fighters have three big lumps contributing to frontal area; two engines and the fuselage.  A single engine fighter only has the engine, with the rest of the fuselage tucked neatly behind it.  The turret fighter isn't as bad; the turret contributes some additional drag, but not as much as the twin-engine design does.  It does, however, add quite a bit of weight, which cripples acceleration even if it has a smaller effect on top speed.  Early-war Japanese and Italian fighters were designed with dogfight  performance above all other considerations, which meant that they had large wings to generate large turning forces, and often had open cockpits for the best possible visibility.  Both of these features added drag, and left these aircraft too slow to compete against aircraft that sacrificed some maneuverability for pure speed.

Drag force rises roughly as a square function of airspeed (throw this formula out the window when you reach speeds near the speed of sound).  Power is equal to force times distance over time, or force times velocity.  So, power consumed by drag will be equal to drag coefficient times frontal area times airspeed squared times airspeed.  So, the power required for a given maximum airspeed will be a roughly cubic function.  And that is assuming that the efficiency of the propeller remains constant!

 

Acceleration is (thrust-drag)/weight.  It is possible to have an aircraft that has a high maximum speed, but quite poor acceleration and vice versa.  Indeed, the A6M5 zero had a somewhat better power to weight ratio than the F6F5 Hellcat, but a considerably lower top speed.  In a drag race the A6M5 would initially pull ahead, but it would be gradually overtaken by the Hellcat, which would eventually get to speeds that the zero simply could not match.

Maximum dive speed is also a function of drag and thrust, but it's a bit different because the weight of the aircraft times the sine of the dive angle also counts towards thrust.  In general this meant that large fighters dove better.  Drag scales with the frontal area, which is a square function of size.  Weight scales with volume (assuming constant density), which is a cubic function of size.  Big American fighters like the P-47 and F4U dove much faster than their Axis opponents, and could pick up speed that their opponents could not hope to match in a dive.

A number of US fighters dove so quickly that they had problems with localized supersonic airflow.  Supersonic airflow was very poorly understood at the time, and many pilots died before somewhat improvisational solutions like dive brakes were added.


Ranking US ace Richard Bong takes a look at the dive brakes of a P-38

Acceleration, top speed and dive speed are all improved by reducing drag, so every conceivable trick for reducing parasitic drag was tried.


The Lockheed P-38 used flush rivets on most surfaces as well as extensive butt welds to produce the smoothest possible flight surfaces.  This did reduce drag, but it also contributed to the great cost of the P-38.


The Bf 109 was experimentally flown with a V-tail to reduce drag.  V-tails have lower interference drag than conventional tails, but the modification was found to compromise handling during takeoff and landing too much and was not deemed worth the small amount of additional speed.


The YAK-3 was coated with a layer of hard wax to smooth out the wooden surface and reduce drag.  This simple improvement actually increased top speed by a small, but measurable amount!  In addition, the largely wooden structure of the aircraft had few rivets, which meant even less drag.


The Donier DO-335 was a novel approach to solving the problem of drag in twin-engine fighters.  The two engines were placed at the front and rear of the aircraft, driving a pusher and a tractor propeller.  This unconventional configuration led to some interesting problems, and the war ended before these could be solved.


The J2M Raiden had a long engine cowling that extended several feet forward in front of the engine.  This tapered engine cowling housed an engine-driven fan for cooling air as well as a long extension shaft of the engine to drive the propeller.  This did reduce drag, but at the expense of lengthening the nose and so reducing pilot visibility, and also moving the center of gravity rearward relative to the center of lift.

 

Designers were already stuffing the most powerful engines coming out of factories into aircraft, provided that they were reasonably reliable (and sometimes not even then).  After that, the most expedient solution to improve speed was to sacrifice lift to reduce drag and make the wings smaller.  The reduction in agility at low speeds was generally worth it, and at higher speeds relatively small wings could produce satisfactory maneuverability since lift is a square function of velocity.  Alternatively, so-called laminar flow airfoils (they weren't actually laminar flow) were substituted, which produced less drag but also less lift.  

 

The Bell P-63 had very similar aerodynamics to the P-39 and nearly the same engine, but was some 80 KPH faster thanks to the new laminar flow airfoils.  However, the landing speed also increased by about 40 KPH, largely sacrificing the benevolent landing characteristics that P-39 pilots loved.

The biggest problem with reducing the lift of the wings to increase speed was that it made takeoff and landing difficult.  Aircraft with less lift need to get to higher speeds to generate enough lift to take off, and need to land at higher speeds as well.  As the war progressed, fighter aircraft generally became trickier to fly, and the butcher's bill of pilots lost in accidents and training was enormous.

 

Turn Rate

 

Sometimes things didn't go as planned.  A fighter might be ambushed, or an ambush could go wrong, and the fighter would need to turn, turn, turn.  It might need to turn to get into a position to attack, or it might need to turn to evade an attack.



Aircraft in combat turn with their wings, not their rudders.  This is because the wings are way, way bigger, and therefore much more effective at turning the aircraft.  The rudder is just there to make the nose do what the pilot wants it to.  The pilot rolls the aircraft until it's oriented correctly, and then begins the turn by pulling the nose up.  Pulling the nose up increases the angle of attack, which increases the lift produced by the wings.  This produces centripetal force which pulls the plane into the turn.  Since WWII aircraft don't have the benefit of computer-run fly-by-wire flight control systems, the pilot would also make small corrections with rudder and ailerons during the turn.

But, as we saw above, making more lift means making more drag.  Therefore, when aircraft turn they tend to slow down unless the pilot guns the throttle.  Long after WWII, Col. John Boyd (PBUH) codified the relationship between drag, thrust, lift and weight as it relates to aircraft turning performance into an elegant mathematical model called energy-maneuverability theory, which also allowed for charts that depict these relationships.

Normally, I would gush about how wonderful E-M theory is, but as it turns out there's an actual aerospace engineer named John Golan who has already written a much better explanation than I would likely manage, so I'll just link that.  And steal his diagram:

E-M charts are often called "doghouse plots" because of the shape they trace out.  An E-M chart specifies the turning maneuverability of a given aircraft with a given amount of fuel and weapons at a particular altitude.  Turn rate is on the Y axis and airspeed is on the X axis.  The aircraft is capable of flying in any condition within the dotted line, although not necessarily continuously.  The aircraft is capable of flying continuously anywhere within the dotted line and under the solid line until it runs out of fuel.

The aircraft cannot fly to the left of the doghouse because it cannot produce enough lift at such a slow speed to stay in the air.  Eventually it will run out of sky and hit the ground.  The curved, right-side "roof" of the doghouse is actually a continuous quadratic curve that represents centrifugal force.  The aircraft cannot fly outside of this curve or it or the pilot will break from G forces.  Finally, the rightmost, vertical side of the doghouse is the maximum speed that the aircraft can fly at; either it doesn't have the thrust to fly faster, or something breaks if the pilot should try.  The peak of the "roof" of the doghouse represents the aircraft's ideal airspeed for maximum turn rate.  This is usually called the "corner velocity" of the aircraft.

So, let's look at some actual (ish) EM charts:

 

 

Now, these are taken from a flight simulator, but they're accurate enough to illustrate the point.  They're also a little busier than the example above, but still easy enough to understand.  The gray plot overlaid on the chart consists of G-force (the curves) and turn radius (the straight lines radiating from the graph origin).  The green doghouse shows the aircraft's performance with flaps.  The red curve shows the maximum sustained turn rate.  You may notice that the red line terminates on the X axis at a surprisingly low top speed; that's because these charts were made for a very low altitude confrontation, and their maximum level top could only be achieved at higher altitudes.  These aircraft could fly faster than the limits of the red line show, but only if they picked up extra speed from a dive.  These charts could also be overlaid on each other for comparison, but in this case that would be like a graphic designer vomiting all over the screen, or a Studio Killers music video.

From these charts, we can conclude that at low altitude the P-51D enjoys many advantages over the Bf 109G-6.  It has a higher top speed at this altitude, 350-something vs 320-something MPH.  However, the P-51 has a lower corner speed.  In general, the P-51's flight envelope at this altitude is just bigger.  But that doesn't mean that the Bf 109 doesn't have a few tricks.  As you can see, it enjoys a better sustained turn rate from about 175 to 325 MPH.  Between those speed bands, the 109 will be able to hold on to its energy better than the pony provided it uses only moderate turns.

During turning flight, our old problem induced drag comes back to haunt fighter designers.  The induced drag equation is C_di = (C_l^2) / (pi * AR * e).  Where C_di is the induced drag coefficient, C_l is the lift coefficient, pi is the irrational constant pi, AR is aspect ratio, or wingspan squared divided by wing area, and e is not the irrational constant e but an efficiency factor.

There are a few things of interest here.  For starters, induced drag increases with the square of the lift coefficient.  Lift coefficient increases more or less linearly (see above) with angle of attack.  There are various tricks for increasing wing lift nonlinearly, as well as various tricks for generating lift with surfaces other than the wings, but in WWII, designers really didn't use these much.  So, for all intents and purposes, the induced drag coefficient will increase with the square of angle of attack, and for a given airspeed, induced drag will increase with the square of the number of Gs the aircraft is pulling.  Since this is a square function, it can outrun other, linear functions easily, so minimizing the effect of induced drag is a major consideration in improving the sustained turn performance of a fighter.

To maximize turn rate in a fighter, designers needed to make the fighter as light as possible, make the engine as powerful as possible, make the wings have as much area as possible, make the wings as long and skinny as possible, and to use the most efficient possible wing shape.

You probably noticed that two of these requirements, make the plane as light as possible and make the wings as large as possible, directly contradict the requirements of good dive performance.  There is simply no way to reconcile them; the designers either needed to choose one, the other, or come to an intermediate compromise.  There was no way to have both great turning performance and great diving performance.

Since the designers could generally be assumed to have reduced weight to the maximum possible extent and put the most powerful engine available into the aircraft, that left the design of the wings.

The larger the wings, the more lift they generate at a given angle of attack.  The lower the angle of attack, the less induced drag.  The bigger wings would add more drag in level flight and reduce top speed, but they would actually reduce drag during maneuvering flight and improve sustained turn rate.  A rough estimate of the turning performance of the aircraft can be made by dividing the weight of the aircraft over its wing area.  This is called wing loading, and people who ought to know better put far too much emphasis on it.  If you have E-M charts, you don't need wing loading.  However, E-M charts require quite a bit of aerodynamic data to calculate, while wing loading is much simpler.
 

Giving the wings a higher aspect ratio would also improve turn performance, but the designers hands were somewhat tied in this respect.  The wings usually stored the landing gear and often the armament of the fighter.  In addition the wings generated the lift, and making the wings too long and skinny would make them too structurally flimsy to support the aircraft in maneuvering flight.  That is, unless they were extensively reinforced, which would add weight and completely defeat the purpose.  So, designers were practically limited in how much they could vary the aspect ratio of fighter wings.

The wing planform has significant effect on the efficiency factor e.  The ideal shape to reduce induced drag is the "elliptical" (actually two half ellipses) wing shape used on the Supermarine spitfire.



This wing shape was, however, difficult to manufacture.  By the end of the war, engineers had come up with several wing planforms that were nearly as efficient as the elliptical wing, but were much easier to manufacture.

Another way to reduce induced drag is to slightly twist the wings of the aircraft so that the wing tips point down.



This is called washout.  The main purpose of washout was to improve the responsiveness of the ailerons during hard maneuvering, but it could give small efficiency improvements as well.  Washout obviously complicates the manufacture of the wing, and thus it wasn't that common in WWII, although the TA-152 notably did have three degrees of tip washout.

The Bf 109 had leading edge slats that would deploy automatically at high angles of attack.  Again, the main intent of these devices was to improve the control of the aircraft during takeoff and landing and hard maneuvering, but they did slightly improve the maximum angle of attack the wing could be flown at, and therefore the maximum instantaneous turn rate of the aircraft.  The downside of the slats was that they weakened the wing structure and precluded the placement of guns inside the wing.


leading edge slats of a Bf 109 in the extended position

One way to attempt to reconcile the conflicting requirements of high speed and good turning capability was the "butterfly" flaps seen on Japanese Nakajima fighters.


This model of a Ki-43 shows the location of the butterfly flaps; on the underside of the wings, near the roots

These flaps would extend during combat, in the case of later Nakajima fighters, automatically, to increase wing area and lift.  During level and high speed flight they would retract to reduce drag.  Again, this would mainly improve handling on the left hand side of the doghouse, and would improve instantaneous turn rate but do very little for sustained turn rate.

 

In general, turn performance was sacrificed in WWII for more speed, as the two were difficult to reconcile.  There were a small number of tricks known to engineers at the time that could improve instantaneous turn rate on fast aircraft with high wing loading, but these tricks were inadequate to the task of designing an aircraft that was very fast and also very maneuverable.  Designers tended to settle for as fast as possible while still possessing decent turning performance.

 

Climb Rate

 

Climb rate was most important for interceptor aircraft tasked with quickly getting to the level of intruding enemy aircraft.  When an aircraft climbs it gains potential energy, which means it needs spare available power.  The specific excess power of an aircraft is equal to V/W(T-D) where V is airspeed, W is weight, T is thrust and D is drag.  Note that lift isn't anywhere in this equation!  Provided that the plane has adequate lift to stay in the air and its wings are reasonably efficient at generating lift so that the D term doesn't get too high, a plane with stubby wings can be quite the climber!

The Mitsubishi J2M Raiden is an excellent example of what a fighter optimized for climb rate looked like.


A captured J2M in the US during testing

The J2M had a very aerodynamically clean design, somewhat at the expense of pilot visibility and decidedly at the expense of turn rate.  The airframe was comparatively light, somewhat at the expense of firepower and at great expense to fuel capacity.  Surprisingly for a Japanese aircraft, there was some pilot armor.  The engine was, naturally, the most powerful available at the time.  The wings, in addition to being somewhat small by Japanese standards, had laminar-flow airfoils that sacrificed maximum lift for lower drag.

The end result was an aircraft that was the polar opposite of the comparatively slow, long-ranged and agile A6M zero-sen fighters that IJN pilots were used to!  But it certainly worked.  The J2M was one of the fastest-climbing piston engine aircraft of the war, comparable to the F8F Bearcat.

The design requirements for climb rate were practically the same as the design requirements for acceleration, and could generally be reconciled with the design requirements for dive performance and top speed.  The design requirements for turn rate were very difficult to reconcile with the design requirements for climb rate.

 

Roll Rate

 

In maneuvering combat aircraft roll to the desired orientation and then pitch.  The ability to roll quickly allows the fighter to transition between turns faster, giving it an edge in maneuvering combat.

Aircraft roll with their ailerons by making one wing generate more lift while the other wing generates less lift.



The physics from there are the same for any other rotating object.  Rolling acceleration is a function of the amount of torque that the ailerons can provide divided by the moment of inertia of the aircraft about the roll axis.  So, to improve roll rate, a fighter needs the lowest possible moment of inertia and the highest possible torque from its ailerons.

The FW-190A was the fighter best optimized for roll rate.  Kurt Tank's design team did everything right when it came to maximizing roll rate.

The FW-190 could out-roll nearly every other piston fighter

 

 

The FW-190 has the majority of its mass near the center of the aircraft.  The fuel is all stored in the fuselage and the guns are located either above the engine or in the roots of the wings.  Later versions added more guns, but these were placed just outside of the propeller arc.

Twin engined fighters suffered badly in roll rate in part because the engines had to be placed far from the centerline of the aircraft.  Fighters with armament far out in the wings also suffered.



The ailerons were very large relative to the size of the wing.  This meant that they could generate a lot of torque.  Normally, large ailerons were a problem for pilots to deflect.  Most World War Two fighters did not have any hydraulic assistance; controls needed to be deflected with muscle power alone, and large controls could encounter too much wind resistance for the pilots to muscle through at high speed.

The FW-190 overcame this in two ways.  The first was that, compared to the Bf 109, the cockpit was decently roomy.  Not as roomy as a P-47, of course, but still a vast improvement.  Cockpit space in World War Two fighters wasn't just a matter of comfort.  The pilots needed elbow room in the cockpit in order to wrestle with the control stick.  The FW-190 also used controls that were actuated by solid rods rather than by cables.  This meant that there was less give in the system, since cables aren't completely rigid.

Additionally, the FW-190 used Frise ailerons, which have a protruding tip that bites into the wind and reduces the necessary control forces:

 

Several US Navy fighters, like later models of F6F and F4U used spring-loaded aileron tabs, which accomplished something similar by different means:



In these designs a spring would assist in pulling the aileron one way, and a small tab on the aileron the opposite way in order to aerodynamically move the aileron.  This helped reduce the force necessary to move the ailerons at high speeds.

Another, somewhat less obvious requirement for good roll rate in fighters was that the wings be as rigid as possible.  At high speeds, the force of the ailerons deflecting would tend to twist the wings of the aircraft in the opposite direction.  Essentially, the ailerons began to act like servo tabs.  This meant that the roll rate would begin to suffer at high speeds, and at very high speeds the aircraft might actually roll in the opposite direction of the pilot's input.



The FW-190s wings were extremely rigid.  Wing rigidity is a function of aspect ratio and construction.

 

The FW-190 had wings that had a fairly low aspect ratio, and were somewhat overbuilt.  Additionally, the wings were built as a single piece, which was a very strong and robust approach.  This had the downside that damaged wings had to be replaced as a unit, however.

 

Some spitfires were modified by changing the wings from the original elliptical shape to a "clipped" planform that ended abruptly at a somewhat shorter span.  This sacrificed some turning performance, but it made the wings much stiffer and therefore improved roll rate.



Finally, most aircraft at the beginning of the war had fabric-skinned ailerons, including many that had metal-skinned wings.  Fabric-skinned ailerons were cheaper and less prone to vibration problems than metal ones, but at high speed the shellacked surface of the fabric just wasn't air-tight enough, and a significant amount of airflow would begin going into and through the aileron.  This degraded their effectiveness greatly, and the substitution of metal surfaces helped greatly.

 

Stability and Safety

 

World War Two fighters were a handful.  The pressures of war meant that planes were often rushed into service without thorough testing, and there were often nasty surprises lurking in unexplored corners of the flight envelope.

 

 

This is the P-51H.  Even though the P-51D had been in mass production for years, it still had some lingering stability issues.  The P-51H solved these by enlarging the tail.  Performance was improved by a comprehensive program of drag reduction and weight reduction through the use of thinner aluminum skin.



The Bf 109 had a poor safety record in large part because of the narrow landing gear.  This design kept the mass well centralized, but it made landing far too difficult for inexpert pilots.



The ammunition for the massive 37mm cannon in the P-39 and P-63 was located in the nose, and located far forward enough that depleting the ammunition significantly affected the aircraft's stability.  Once the ammunition was expended, it was much more likely that the aircraft could enter dangerous spins.

 

The cockpit of the FW-190, while roomier than the Bf 109, had terrible forward visibility.  The pilot could see to the sides and rear well enough, but a combination of a relatively wide radial engine and a hump on top of the engine cowling to house the synchronized machine guns meant that the pilot could see very little.  This could be dangerous while taxiing on the ground.


 

[LostCosmonaut]

Could you elaborate more on the difficulties associated with a setup like the 335? I imagine cooling the aft engine would be a big one. That engine layout seems like a pretty ingenious way to minimize frontal area for a twin, while also improving roll rate.

[Xlucine]

Takeoff/landing is harder - the maximum you can pitch up on takeoff is limited by the rear propeller, and the pitch you hold after the flare on landing is also similarly limited. Late war turbocharged double wasps were pushing the same ballpark power as both do335 engines combined, which is a much better idea, and the he119 approach with the later engine would probably achieve a similar result

[Bronezhilet]

25 minutes ago, LostCosmonaut said:

Could you elaborate more on the difficulties associated with a setup like the 335? I imagine cooling the aft engine would be a big one. That engine layout seems like a pretty ingenious way to minimize frontal area for a twin, while also improving roll rate.

Bailing out became a little tricky. 

[Scolopax]

I'm curious about the Hurricane here.  I realize the battle of Britain probably inflates its fame a bit more than its worth, but what was so wrong with the plane?  The only thing I'm aware of is that it was somewhat outdated by the time it was seeing action and that its armament of .30 cals was lackluster.  I imagine the construction has something to do with it since it was pointed out.

 

Also, the Spitfire's landing gear seems pretty narrow like the 109, if not a little shorter in length.  It did not have any such issues with landing safety, correct?

[Collimatrix]

5 hours ago, LostCosmonaut said:

Could you elaborate more on the difficulties associated with a setup like the 335? I imagine cooling the aft engine would be a big one. That engine layout seems like a pretty ingenious way to minimize frontal area for a twin, while also improving roll rate.

 

There's a book from 1980 called "Luftwaffe Test Pilot" which is a translation of an original German memoir by a test pilot who was primarily tasked with flying captured Allied aircraft.  He gets his hands on a DO-335 later on.  The aircraft seemed to be generally sound, and all the problems likely soluble, but the engine configuration did lead to some unusual technical hangups.

For instance, you don't want the aircraft's compass to be too close to the engine.  Spark-ignition engines create a good deal of EM interference around themselves from the spark plugs, so they screw with things like compasses.  In the DO-335 anywhere in the fuselage constituted being too close to the engine.  So the compass ended up way out in one of the wings.  This ended up causing other problems, but I don't recall the specifics and don't have the book handy.  The rear prop is also fairly far from the engine and mounted on an extension shaft.  Shafts like those were often the source of vibration problems, although it was nothing that couldn't be cured eventually, based on the hordes of P-39s that Bell made.

From a more theoretical perspective, placing an engine at the rear like that is going to move the center of gravity way back, since the engine was usually the single heaviest thing in a fighter.  The wings on the DO-335 are very slightly aft swept, probably to compensate for this.  I would be curious to know where all the fuel and ammo was on the DO-335, and whether consuming them would be likely to cause any stability issues.  The rear prop is also working in disturbed airflow, both from the front prop and the fuselage, so there are some potential vibration/oscillation issues there.  On the debit side, as long as the props counter-rotate and are sized correctly, the push-pull configuration should have a small efficiency bonus from the rear prop canceling out the spiraling of the airflow from the front prop.

 

I don't get the impression that any of the unique technical challenges of the push-pull configuration could be solved.  However, by that time jets existed.

 

1 hour ago, Scolopax said:

I'm curious about the Hurricane here.  I realize the battle of Britain probably inflates its fame a bit more than its worth, but what was so wrong with the plane?  The only thing I'm aware of is that it was somewhat outdated by the time it was seeing action and that its armament of .30 cals was lackluster.  I imagine the construction has something to do with it since it was pointed out.

 

Also, the Spitfire's landing gear seems pretty narrow like the 109, if not a little shorter in length.  It did not have any such issues with landing safety, correct?

 

According to the encyclopedia of historical aviation knowledge that is Armstong and Miller, the hurricane was a shit plane:
 

And yes, by accounts the Spitfire's narrow gear was a liability while landing, as was it's somewhat poor forward visibility.  The Bf 109 had it a little worse; the gear was both narrow, and somewhat prone to breaking.  I can't imagine the pair of big brass ones that a pilot would need to contemplate landing a Seafire on a carrier.  They had to come up with all sorts of tricks to make it work, like flying a slalom landing approach so they could see where the carrier was!

[Jeeps_Guns_Tanks]

Is the P-38 the exception to to the heavy fighters being a failure  rule? It was a very successful fighter and well like by most users, 8th air force guys who couldn't figure out how to maintain it aside.

 

[Collimatrix]

Yeah, P-38 is one of the exceptions.  Lockheed did such a good job streamlining it that it really didn't have a speed or drag disadvantage compared to contemporary fighters.  At higher altitudes, it actually had a big speed advantage.

According to this source, the thrust relative to drag on the P-38 was quite competitive:

 

On top of that, the P-38 had a hidden edge in acceleration that the raw power/weight figures don't show.  Because the props were counter-rotating the pilot could just firewall the throttles if he wanted to go fast.  The pilot didn't have to worry about torque, p-factor or adverse yaw, it was just acceleration.

 

On the earlier models the roll rate suffered, as you might expect from an aircraft with two heavy engines far out from the centerline.  However, the hydraulically boosted ailerons on the J apparently fixed this, and the J could roll at high speeds with nearly any other fighter.

 

So, by the last models, the P-38 didn't really suffer from most of the vices of twin-engined fighters because Lockheed just threw enough technology at it that the problems went away.

[Belesarius]

Would you add the Mossie to the list of exceptions Colli?

 

[Scolopax]

I can think of a several aircraft (F7F, Westland Whirlwind, and more) too, but I suppose I'll ask first if there's much or any distinction between a twin-engine fighter and a heavy fighter.  I feel armament plays a role here.

[Jeeps_Guns_Tanks]

6 minutes ago, Collimatrix said:

Yeah, P-38 is one of the exceptions.  Lockheed did such a good job streamlining it that it really didn't have a speed or drag disadvantage compared to contemporary fighters.  At higher altitudes, it actually had a big speed advantage.

According to this source, the thrust relative to drag on the P-38 was quite competitive:

 

On top of that, the P-38 had a hidden edge in acceleration that the raw power/weight figures don't show.  Because the props were counter-rotating the pilot could just firewall the throttles if he wanted to go fast.  The pilot didn't have to worry about torque, p-factor or adverse yaw, it was just acceleration.

 

On the earlier models the roll rate suffered, as you might expect from an aircraft with two heavy engines far out from the centerline.  However, the hydraulically boosted ailerons on the J apparently fixed this, and the J could roll at high speeds with nearly any other fighter.

 

So, by the last models, the P-38 didn't really suffer from most of the vices of twin-engined fighters because Lockheed just threw enough technology at it that the problems went away.

 

It was very pricey, but the late model J and L birds were reliable and very long legged. The 475th Fighter group was flying into Indo-China, (vietnam) from the Philippines late in the war looking for kills. The J and L birds had extra internal wing fuel tanks, and could lug a pair of 300 gallon drop tanks. Plus Lindberg had come though and shown them had to really stretch the P-38s range out, by running high manifold pressure with very lean mixtures. 

 

Things the guys in Europe never figured out. 

[LostCosmonaut]

The 110's issues were definitely compounded by the rear gunner and all the weight that that added (which the F7F and P-38 didn't have). I wouldn't call the Whirlwind a success, but that's because it was handicapped by its engines, not any glaring design flaw that I can think of.

[Jeeps_Guns_Tanks]

The V1710s power growth and the turbo system in the P-38 made it very cutting edge for when it first flew. One of it's main flaws, the mess that was the cockpit was never address, unlike in the Corsair and P-47.  

[Collimatrix]

3 hours ago, Belesarius said:

Would you add the Mossie to the list of exceptions Colli?

 

 

The Mosquito was certainly an excellent aircraft, but I'm not sure that it was an excellent air superiority fighter in the sense that it could tangle with other air superiority fighters and prevail.  It seems more like a JU-88 analogue, only made of wood and better, rather than something like a P-38, which through careful engineering stood a good chance against much lighter adversaries.  I have seen claims that it was both faster and more maneuverable than the Spitfire.  Faster would depend on exactly which mark of Spit, but any Spit that was slower than a Mosquito would have about half the wing loading, so I'm dubious that its turn performance could have possibly been better.  I also have doubts about the G limits of the wooden structure, but I haven't found anything specifically addressing that.

 

3 hours ago, Scolopax said:

I can think of a several aircraft (F7F, Westland Whirlwind, and more) too, but I suppose I'll ask first if there's much or any distinction between a twin-engine fighter and a heavy fighter.  I feel armament plays a role here.

 

By "heavy fighter" I was thinking of the pre-war concept.  The Germans called the idea the zerstorer, but other nations tried similar concepts like the Dutch Fokker G.I and the French Potez 630.  A fair number of these aircraft actually proved useful during the war, just not in their original role.  The Germans went into the war convinced that the 110 could tangle with single engine fighters, and after they hacked their way through a lot of obsolescent French and Polish aircraft, they remained convinced.  Fighting the RAF, who had far more modern aircraft and rage born of desperation was a very unpleasant wake-up call.  The 110 wasn't completely useless after that, along with the JU-88 it did most of the Luftwaffe's heavy lifting as a radar-equipped night fighter.  But for fighting single-engine fighters that were actually made of metal, and had engines over 1000 horsepower, retractable landing gear and enclosed cockpits?  Not a chance.

 

The F7F would probably have done fine in the Pacific against single engine fighters for the simple reason that Japanese production of anything that wasn't an A6M or Ki-43 was pathetic.  Against their more modern aircraft like the N1K2J and Ki-84, I'm not as sure.  But the production of those types was pitiful, so it really didn't matter.  Likewise, a hypothetical European theater Tigercat would mostly be up against fundamentally older and slower aircraft.  The things that might reasonably have given it trouble just weren't terribly common.

 

The Whirlwind is an interesting case.  There does seem to have been some effort put into mitigating the inherent aerodynamic penalties of the twin-engine configuration.  The low-drag radiator design was somewhat similar to the one found on early P-38s.  Also, apparently the flaps doubled as radiators (?!).

For a time, it could hack it as a fighter simply because it had unmatched firepower and it was faster than a Bf 109E4.  However, aside from having Frise-type ailerons I can't find any reference to any means of improving the roll rate.  So once the improved Bf 109F variants that could keep up with the Whirlwind showed up, it was in trouble, since it would probably have a slower roll rate and, if the wing loading is anything to go by, inferior turn performance.  It could still obliterate anything stupid enough to get in front of it, but being no faster and less maneuverable, it couldn't force single engine fighters to get in front of it.  By that point the Whirlwind was mostly being used for ground attack anyway.

[LostCosmonaut]

Looks like they considering putting a variable incidence wing on the 335 at one point, which is one way to get around the rear prop clearance issue.

 

 

Don't think I'd trust 1945 German engineering on that though.

[Priory_of_Sion]

I'm personally curious about trade-offs concerning range and loitering times against other characteristics. I don't know quite as much about planes as I do armored vehicles, but having aircraft in the air longer or have them being able to go farther seems like it would be just as important as its dogfighting capabilities. 

[Bronezhilet]

On 11/12/2017 at 7:09 PM, LostCosmonaut said:

Looks like they considering putting a variable incidence wing on the 335 at one point, which is one way to get around the rear prop clearance issue.

 

 

Don't think I'd trust 1945 German engineering on that though.

Also, a tail wheel instead of a nose wheel.

[Sturgeon]

On 11/11/2017 at 12:08 AM, Collimatrix said:

The Mitsubishi J2M Raiden is an excellent example of what a fighter optimized for climb rate looked like.


A captured J2M in the US during testing

The J2M had a very aerodynamically clean design, somewhat at the expense of pilot visibility and decidedly at the expense of turn rate.  The airframe was comparatively light, somewhat at the expense of firepower and at great expense to fuel capacity.  Surprisingly for a Japanese aircraft, there was some pilot armor.  The engine was, naturally, the most powerful available at the time.  The wings, in addition to being somewhat small by Japanese standards, had laminar-flow airfoils that sacrificed maximum lift for lower drag.

The end result was an aircraft that was the polar opposite of the comparatively slow, long-ranged and agile A6M zero-sen fighters that IJN pilots were used to!  But it certainly worked.  The J2M was one of the fastest-climbing piston engine aircraft of the war, comparable to the F8F Bearcat.

 

Ah yes, the J2M "Pocket Rocket".

[Collimatrix]

On 11/12/2017 at 3:15 PM, Priory_of_Sion said:

I'm personally curious about trade-offs concerning range and loitering times against other characteristics. I don't know quite as much about planes as I do armored vehicles, but having aircraft in the air longer or have them being able to go farther seems like it would be just as important as its dogfighting capabilities. 

 

This is an interesting topic.

Modern fighter aircraft have very little free space in them.  Almost every cubic centimeter inside is filled with something:

 

There are gigantic bays crammed full of electronics with just enough space around them to ensure adequate air circulation, and there's fuel stuffed into every available space to feed the thirsty jet engines. 

 

 

Second World War fighters are quite a bit more open inside.  Above is a shot of the inside of the rear fuselage of a Spitfire.  As you can see, there's a whole lot of nothing back there.

 

I'll skip a detailed derivation of it, but the Breuget Range Equation explains that the cruising range of an aircraft is a linear function of cruise airspeed, lift to drag ratio, specific fuel consumption, and the natural log of the fully fueled weight over the empty weight.  This looks sort of like the Tsiolkovsky Rocket Equation, and I suppose it's a distant relative.

So why not just cram every single corner of the fighter full of fuel?  That ought to do the trick!

Very simply, they couldn't.

 

Back in World War Two the designers didn't have the luxury of computer-controlled everything.  That means that, if the aircraft had multiple fuel tanks, the pilot needed to manually select which ones were feeding to the engine.  It meant that flight computers couldn't automatically re-trim the aircraft if the balance shifted in flight.  Also, they didn't have fancy fly-by-wire systems, so the aircraft had to be statically stable with the center of gravity in front of the center of lift:



Moreover, since we're talking about fighters here, the center of lift has to be fairly close to the center of gravity, or the fighter will suffer from pitch stiffness and the pilot will really have to pull hard on the stick to get the nose to move.  Again, the vast majority of WWII fighters relied on the pilot's muscles to actuate the flight controls, so having heavy control forces was out of the question.

 

All this together meant that the fuel tanks in a Second World War fighter could really only be placed close to the center of gravity so that consuming the fuel would affect the stability and trim of the aircraft as little as possible.  Ideally the ammunition for the guns would be near the center of gravity as well for the same reason.

On a typical WWII fighter the center of lift will be located somewhere a little bit back from the front quarter mark of the chord length of the wings.  Airfoils generally have their aerodynamic center around 25% of of the Mean Aerodynamic Chord, but the horizontal stabilizers push it back a little further.  The center of gravity will be in front of that.  So, basically, a designer would want the fuel tanks to be centered at about the leading edge of the wing.

 

That's the reason that most WWII fighters only have fuel tanks in the fuselage, often immediately behind the engine or under the pilot.  Surprisingly few have fuel tanks in the wings, given the amount of volume the wing represents.  Generally speaking the wings were already full of landing gear, guns and ammo, and sticking gas tanks in there wasn't worth the bother.  It may have been possible to put auxiliary fuel tanks in the wings further outboard of the guns, but this would have reduced roll rate at least until that fuel was consumed.  I'm not aware of any designs that did this, but that doesn't mean they didn't exist.

One big exception is the P-51 Mustang.  The P-51 had those wonderful laminar-flow wings that did everything except actually make the airflow laminar.  Laminar flow airfoils can be much larger for a given amount of drag than their conventional counterparts, and the P-51 had gigantically thick wings.  This meant that there was plenty of room for guns, ammo, landing gear, and a generous amount of fuel:

 

So, practically speaking, most designers were stuck with the amount of internal fuel they could pack under the pilot and behind the engine.

Increasing lift to drag ratio typically optimizes for aircraft with very smooth, cigar-shaped fuselages and long, skinny wings.  So, basically B-29 shaped sorts of things.  That synergizes well with optimizing for sustained turn rate, but as we've seen, optimizing for sustained turn rate conflicts with just about everything else.

 

Most WWII engines tended to have samey fuel efficiency, although the British sleeve-valve engines had a small edge in fuel economy.  The Soviets did try using diesel engines in bombers, but for a variety of reasons this didn't really work.  This may not have been a total loss; according to some sources the V-2 diesel in the... well, just about every Soviet medium and heavy tank was derived from a diesel intended for aircraft.  I've never seen the final word on whether that's true or not.  @EnsignExpendable, do you know?

 

Flying at higher altitude tended to result in better range.

 

At the end of the day, the best way to solve the problem was probably drop tanks.

[Jeeps_Guns_Tanks]

Don't forget the wonderful for making the plane handle poorly, so it was drained before the drop tanks, behind the pilot fuel tank in the P-51D.

[EnsignExpendable]

Get a load of this loser and his stable airframe

 

That is partially true @Collimatrix. The V-2 was initially designed as a tank engine for the BT series, under the index BD ("fast diesel"). The development of the aircraft variant began after it was tested in a tank. The idea was to unify the aircraft and tank versions as much as possible, but the plane that was supposed to use the engine was obsolete by the time production got off the ground. 

[Collimatrix]

3 hours ago, Jeeps_Guns_Tanks said:

Don't forget the wonderful for making the plane handle poorly so it was drained before the drop tanks behind the pilot fuel tank in the P-51D.

 

I haven't found the capacity of that rear tank, but yes, by all accounts the pony was... squirrely until it was empty.  Late model FW-190s had a similar fuel tank behind the pilot, and I would bet they emptied that one first too.

[Jeeps_Guns_Tanks]

85 gallons. 

 

[Collimatrix]

So that's about 500 pounds placed about four feet behind the CG.  Yep, that could cause some issues.

[SuperComrade]

16 hours ago, Collimatrix said:

 The Soviets did try using diesel engines in bombers, but for a variety of reasons this didn't really work.  This may not have been a total loss; according to some sources the V-2 diesel in the... well, just about every Soviet medium and heavy tank was derived from a diesel intended for aircraft.  I've never seen the final word on whether that's true or not.  @EnsignExpendable, do you know?

The V-2 is not derived from an aircraft diesel engine as far as I know. However, the 5TD family was designed by Aleksandr Charomskiy, and it is related to the Soviet Charomskiy M-30 and M-40 aircraft diesel engines. They were in turn inspired by the Junkers Jumo 205.

The M-30/ACh-30 would eventually be made workable on the Yermolayev Yer-2 by the end of the war, but by that time jet engines and turboprops were coming into service and there was very little point in continuing to invest in diesel engines for aircraft.