Performance limitations of WW-2 aircraft

[dracos]

Hello all,
While looking up different aircraft types, I came across a number of older threads that left me pondering questions about aircraft performance. Rather than ask in each individual thread, I'll start a brand new one.

What are the relationships between aircraft weight, climb rate, and speed? I know the lighter the plane, the faster it will fly (forward) and climb. If these relationships were graphed, would they be smooth curves, look like hills and valleys, logarithmic-shaped, etc? This question was inspired by the Bearcat's world-breaking climb and could that be possible for a stock aircraft. Is there a point past which the relationship between weight/mass and climb rate approaches a vertical line on a graph?

Could a WW-2 era jet go supersonic with the existing airframes? For example, if the Me-262 had powerful enough engines, could it go supersonic in level flight, or would it break up, experience some effects to stop further acceleration, etc? I know aircraft like the Hunter and maybe the Mig-17 could go supersonic in a dive.

Another climbing question. Is there a theoretical maximum climb rate for prop aircraft?

Thanks,
dracos

[GregP]

Hi Dracos,

First, weight has nothing to do with climb rate. Second, I am making the assumption of at least competent design. That is, I assume, in the following, that no designer will saddle his pet fighter with a very poor choice of airfoil or poor choice of propeller section. Poor choices of cooling or airfoil will make the following text invalid.

Climb rate: Assuming decent design, climb rate is almost directly tied to the power to weight ratio. That is, horespower per pound or kilowatt per kilogram. Any fighter that has a power to weight ratio of 4 to 5 pounds per horsepower will climb better than another fighter with a higher power loading.

For your reference, most fighters have the worst power to weight ratio at gross weight. Combat weight is usually about 50% of the way between power to weight when empty and power to weight when at gross weight.

Maneuverability is almost directly related to wing loading. That is, pounds per square foot or kilograms per square meter. Most WW2 fighters were in the range of 32 - 45 pounds per square foot. The Spitfire and Zero were at the bottom of that range or less and were VERY maneuverable. Most of the German fighters were at the higher end of that range, and could not turn with a Spitfire. Most American fighters were in the 35 - 42 pounds per square foot range.

Rate of roll is tied to wing dihedral, the aileron airfoil, the control stick leverage ratio, and to the amount of aerodynamic balance (aileron surface forward of the hinge point) on the ailerons.

Service ceiling is directly tied to the engine performance, but I am assuming you mean aircraft designed for higher altitudes for Europe. If the engine were sufficient (2-stage, 2 or 3-speed supercharger), then high altitude capability and maneuverability is tied directly to span loading. That is pounds per foot of span or kilograms per meter of span. Lower is better, just like in power loading and power to weight ratio.

There is no real theoretical maximum climb rate, but there is a practical one.

The limiting speed for a very clean aircraft comes somewhere between when the propeller tips go supersonic and when 75 - 80% of the blade is supersonic, depending on properller section design (airfoil). Practically speaking, around 550 to 580 mph is very near the best that can be expected, thopugh 600 mph MAY be possible.

Rate of climb is really vertical speed. If a fighter can sustain 105 mph in a 45° climb, then it will be climbing at about 6,500 feet per minute. Since VERY few piston aircraft can manage than climb rate, it follows that the reason is a need for a lower power to weight ratio.

In WW2, aeronautics was not well enough understood to get much more than 480 mph or so. Today, there are no high-power piston engines being made anywhere except for rebuilt WW2 powerplants.

If someone DID make one and if there were interest, I believe a 600 mph propeller-driven piston aircraft could be designed. The real probelm is that there is nobody willing to spend the money to do better than build up a WW2 fighter since they were the best-performing piston-driven aircraft ever made by man.

The current propeller-driven, piston-powered world speed record is 529+ mph by Rod Lewis' Grumman Bearcat named "Rare Bear." There is very little "Bearcat" left in Rare Bear. The engine is different, the wings have been profiled differently, it uses a spray bar and ADI like a small river, and the aircraft was more than 80 knots over the "stock" design limiting speed when they set the record. That means the aircraft was very near the limits of controllability. If it diverged from a more or less straight path, it may well have disintegrated.

Also, be advised that most WW2 aircraft usually never got anywhere NEAR their published maximum speeds. The maximums quoted were for a clean aircraft (no ordnance or external stores), waxed, just tuned up, and at the engine's critical altitude (altitude where power starts falling off). Mostly, the WW2 fighters, when at low altitudes, were 290 mph to 350 mph aircraft. Some were slower down low, but faster up high.

Hope this helps ...

[Wuzak]

Hi Greg,

Just a couple of remarks that seem contradictory:

Hi Dracos,

First, weight has nothing to do with climb rate.

Climb rate: Assuming decent design, climb rate is almost directly tied to the power to weight ratio. That is, horespower per pound or kilowatt per kilogram. Any fighter that has a power to weight ratio of 4 to 5 pounds per horsepower will climb better than another fighter with a higher power loading.



You say that weight has nothing to do with climb rates, but then go on to say that climb is tied to the power to weight ratio.

Presumably if you have two aircraft with aerodynamically identical airframes, and using the same engine (same power), but one is lighter than the other it will climb better than the heavier one?




Service ceiling is directly tied to the engine performance, but I am assuming you mean aircraft designed for higher altitudes for Europe. If the engine were sufficient (2-stage, 2 or 3-speed supercharger), then high altitude capability and maneuverability is tied directly to span loading. That is pounds per foot of span or kilograms per meter of span. Lower is better, just like in power loading and power to weight ratio.

There is no real theoretical maximum climb rate, but there is a practical one.
Rate of climb is really vertical speed. If a fighter can sustain 105 mph in a 45° climb, then it will be climbing at about 6,500 feet per minute. Since VERY few piston aircraft can manage than climb rate, it follows that the reason is a need for a lower power to weight ratio.




Just to clarify, when you say power loading do you mean weight to power ratio, as in lb/hp or kg/kW, which is the inverse of power to weight ratio?

Therefore, for better climb I presume you would need a higher power to weight ratio which is equivalent to a lower power loading?

[GregP]

Hi Wuzak,

I beklieve I specified pounds per horsepower, which is weight to power but you are right, I said it backwards.

As for weight, it makes a difference if the same engine power is used, but that is a simplistic view of weight. If you simply remove the 2,500 HP R-2800 from a Bearcat and install an R-3350 of 4,000 HP, then you radically alter the weight to power ratio and it climbs like tere is no tomorrow.

So, I stand by what I said. Weight has very little to do with climb rate uless you have the unfortunate situation of being tied to a partcular engine. Then weight becomes important.

To clarify, the vehicle with the highest climb rate in the world is also the fastest aircraft, and is one of the heaviest at liftoff. That would be the Space Shuttle at Mach 25. Since the weight was fixed, NASA added some "horsepower" in the form of SRBs (Solid Rocket Boosters) tacked onto the side of the Shuttle.

[Lightning]

Hi Greg,

Another fine, in-depth posting of the caliber that I have come to expect from you. Just a few comments:


Rate of roll is tied to wing dihedral, the aileron airfoil, the control stick leverage ratio, and to the amount of aerodynamic balance (aileron surface forward of the hinge point) on the ailerons.

The distribution of the weight (mass) around the roll axis is also important--the closer, the better. This is one of the drawbacks of my beloved P-38.

There is no real theoretical maximum climb rate, but there is a practical one.

Rate of climb is really vertical speed. If a fighter can sustain 105 mph in a 45° climb, then it will be climbing at about 6,500 feet per minute. Since VERY few piston aircraft can manage than climb rate, it follows that the reason is a need for a lower power to weight ratio.

Strictly speaking, power-to-weight (more accurately thrust-to-weight) ratio is the single limiting factor only in a vertical climb, i.e. when the only force opposing weight is thrust. At climb angles between 0° and 90°, the lift of the wings plays an important role. In fact, an airplane is capable of gaining altitude (climbing) at a constant rate while maintaining a level attitude (i.e. a zero degree climb angle), depending only on the lift of its wings to gain altitude. In that situation, there is a zero vertical component of engine thrust. I remember seeing films of fully loaded B-52s lifting off the runway in a horizontal attitude and gaining several hundred feet before establishing a climbing angle.

Of course, the only way an airplane can sustain a constant vertical climb is to have a thrust-to-weight ratio of at least 1:1. No WWII propeller-driven fighter had this kind of power. I guess the "fighter" that came closest was the rocket-powered Me163 "Komet." I'm not with my books right now, so I don't know its thrust-to-weight ratio. Corsarius could certainly tell us, that being his favorite plane.

Regards,
Lightning

Regards,
Lightning

[GregP]

Yeah, it depended on what proof booze was used to power it .... :-)

Vodka doesn't climb as well as Cognac ...

[Lightning]

Hi Greg,


Vodka doesn't climb as well as Cognac ...

But it gets you higher. :D

Regards,
Lightning