2
$\begingroup$

So, I just noticed that typical WWII piston engine fighter aircraft had a power to weight ratio of around 300W/kg, even at gross weight and altitude. This means that if we assume that an aircraft has an L/D of 10, and is allowed to fly at 80% throttle, we get a cruise speed of 240m/s (534 mph).

If we accept the situation as above, it would seem that the practical limit to speed was aerodynamics. This can be solved with swept wings and ducted fans. But this was never done.

Why was this not done? What am I missing?

$\endgroup$
10
  • 1
    $\begingroup$ How are you going from L/D to predicted cruise speed? $\endgroup$ Commented Feb 4 at 15:31
  • $\begingroup$ @quietflyer speed = gravity × D/L × P/M $\endgroup$ Commented Feb 4 at 15:44
  • 1
    $\begingroup$ "These can be solved with swept wings and ducted fans.". And that's pretty much what happened. Oh, and coincidentally, right around that same time they also replaced heavier piston engines with lighter turbine engines, gaining further performance advantages. $\endgroup$ Commented Feb 4 at 15:57
  • 1
    $\begingroup$ At the end of WWII, aircraft development was done on paper with slide rules and a good dose of "that looks pretty good, build it". Whereas today's aircraft development is done with computers, CFD and mountains of red tape that significantly reduce the speed of development. If you want to see "rather long" development times, look at something like the B1, F22 or F35, then compare that to the B52, U2, and SR71. $\endgroup$
    – FreeMan
    Commented Feb 5 at 16:30
  • 1
    $\begingroup$ Well, they nearly did. For example, the Soviet Yak-9U, American P-51 and German Bf.109K-4 piston fighters were able to reach 700-720 km/h (430-450 mph or 380-390 knots) at around 4000 m. $\endgroup$
    – trolley813
    Commented Feb 6 at 19:25

3 Answers 3

9
$\begingroup$

What am I missing?

The contribution of zero lift drag to overall drag at high speed. L/D drops to much lower values than 10 at the top speed of piston-powered airplanes.

Let's take an example: Given is the power loading (56.8 kW/m²) and the zero lift drag coefficient of 0.028. How fast can this airplane fly at an altitude of 6000 m (air density $\rho$ there is 0.66012 kg/m³) when its propeller efficiency is 85%?

$$P = \frac{D\cdot v}{\eta_{Prop}} \Leftrightarrow \frac{\rho\cdot c_D\cdot S}{2\cdot\eta_{Prop}}\cdot v^3 \Leftrightarrow v = \sqrt[\Large{3}\;]{\frac{2\cdot P\cdot\eta_{Prop}}{\rho\cdot c_D\cdot S}}$$

If you plug in the numbers (don't forget to use W, not kW!), the result will be 173.55 m/s or 624.8 km/h. If I now tell you the wing area of only 16.4 m², can you guess which airplane I have used?

56.8 times 16.4 is 932 kW or 1250 hp, which is the power output of a DB 605 A1 in 5800 m. And the poor drag coefficient had been confirmed in the large windtunnel in Chalais-Meudon (on an earlier version, however). So this is a Me-109 in a version between G1 and G8. If we now look up the top speed at that altitude, we get 626 km/h in 6100 m. This is very close and should demonstrate that induced drag is completely unimportant at top speed.

This also means that speed will only increase with the third root of power. To get to 500 mph which is 805 km/h or 223.5 m/s, engine power needs to more than double to 2660 hp, neglecting any mass increase or Mach effects on propeller performance! With the usual power loading of contemporary piston engines of 0.5 kg/hp, this massive engine realistically needs to have a much larger airframe, so we are fighting diminishing returns.

You start from the wrong assumptions. L/D at top speed is much lower than 10.

$\endgroup$
5
  • $\begingroup$ Guess I should have made my comment aviation.stackexchange.com/questions/102809/… into an actual answer, that seems to be the point of this answer and I think it is correct -- $\endgroup$ Commented Feb 6 at 0:48
  • 1
    $\begingroup$ Wait a sec, why on earth would you use wing area? $\endgroup$ Commented Feb 6 at 2:46
  • $\begingroup$ @Abdullah ¿What are you asking? Please be more specific! $\endgroup$ Commented Feb 7 at 8:42
  • $\begingroup$ You used wing area to get the drag. Whereas I would expect you to use frontal area. Is it because pressure drag us insignificant? $\endgroup$ Commented Feb 7 at 11:47
  • $\begingroup$ I used power loading (power per wing area) as the input, and a rather high value of it, too. In the formula I have power P and area S on both sides of the fraction. If you only double engine size and weight, the unchanged wing area will become too small for decent take-off and landing characteristics, but will help in going faster (remember the 209 V1 which held the speed record for a while: It had a highly tuned DB601 and a smaller wing than the regular 109). $\endgroup$ Commented Feb 7 at 18:08
6
$\begingroup$

What am I missing?

The historical and technological development.


Let's start with the historical one.

The benefits of a swept wing had already been known at least since 1935 when A. Büsemann presented a paper at the Fifth Volta Conference in Rome about the advantages of a swept wing at supersonic speed (Busemann, A. - "Aerodynamicher Auftrieb bei Überschall Geschwindigkeiten" Luftfahrtforschung, Bd 12, Nr 6, October 3, 1935, pp. 210-220).

Apparently nobody among the attendees (of several nationalities) was able to appreciate that discovery, except the German government that classified that paper. In the following years, further theoretical and practical research was carried out in Germany that verified the property of wing sweep in delaying the onset of the compressibility drag. The same research was independently conducted in the USA (although with some ten years of delay) and resulted in the seminal paper "Wing plan forms for high-speed flight" by Robert T. Jones.

So, from an historical point of view only the Germans knew/pursued the advantages given by a swept wing design and only toward the end of the war.


Anyway, this knowledge alone would have been completely useless without another technological improvement of paramount importance. The speed seen by a propeller blade is given by the composition of its rotating speed and its flying speed; being them perpendicular the total speed is simply $\sqrt{V²_{rot}+V²_{fly}}$. When this speed reaches transonic values, aerodynamic drag and pitching moment of the blades increase exponentially. The only way to increase flying speed avoiding transonic effect would be by reducing the rotating speed but unfortunately this would also reduce the thrust generated by the propeller. So getting both lot of thrust and high flying speed is something that couldn't be be achieved with the propeller technology of that time: it's not a matter of power, it's a matter of limits of physics (today, as pointed out by @Pilothead, much higher speed can be achieved).

The only way to overcome this limitation would have been via a completely new propulsion system: jet engine arrived just at the right moment. Swept wing and jet engine eventually came together towards the end of the war in the Messerschmitt Me-262.

$\endgroup$
8
  • $\begingroup$ Would a (piston powered) ducted fan still suffer at transonic tip speeds? $\endgroup$ Commented Feb 4 at 21:51
  • 1
    $\begingroup$ @CamilleGoudeseune: the speed seen by a blade is given by the composition of its rotating speed and its flying speed. Being them perpendicular: $V_{tip}=\sqrt{V²_{rot}+V²_{fly}}$ no matter if there's a duct or not. Anyway a ducted fan would produce some 30% more thrust at the same power but it would be also also more susceptible in respect to the airflow orientation. $\endgroup$
    – sophit
    Commented Feb 5 at 4:47
  • $\begingroup$ The ATR42 is a poor example of physics limited prop plane speed; its competitor the Dash8-400 cruises at 600kph by using more fuel in an updated design. The ATR is more popular for its fuel efficiency. The Tu95 cruises above 700kph and the Rare Bear F8F Bearcat hit 850kph. The X84H 'Thunderscreech' disputedly hit 1000kph. Prop planes are physics limited, but not at the speed of an ATR. $\endgroup$
    – Pilothead
    Commented Feb 5 at 15:19
  • 1
    $\begingroup$ @Pilothead: yes, and the Piaggio P-180 is actually "the fastest propeller-driven aircraft with speed of 927.4 km/h (576.3 mph; 500.8 kn)". I've chosen the not so advanced ATR to have a somewhat fairer comparison with the technology of the '40s 😉 $\endgroup$
    – sophit
    Commented Feb 5 at 16:23
  • $\begingroup$ That P180 record is ground speed, not airspeed. Its high speed cruise is 750kph. $\endgroup$
    – Pilothead
    Commented Feb 5 at 17:11
1
$\begingroup$

Another effect which must be considered is that when the vector-resolved airspeed at the tip of a propeller blade which is spinning and translating through the air gets close to mach 1, the drag force on it goes up and the prop tip's thrust generation falls off and it becomes a noise generator instead of a propulsion generator. Spinning the prop faster than that just moves the mach 1 point closer to the prop hub and renders more of the blade less effective. So you have to add blades to add thrust in addition to sweeping their tips.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .