I will survive!

[Brooke]

In level flight, T - D = m * a, where a is acceleration, m is mass of aircraft, T is thrust, and D is drag; or a = (T - D) / m.  T = thrust of engine, D = drag = 0.5 * C_D * rho * v^2 * S, where C_D = coefficient of drag, rho = density of air, v = velocity of aircraft, S = wing area.  Let me define Z as 0.5 * rho * v^2 * S.  Then D = C_D * Z.   Also from aerodynamics of airfoils, C_D = C_D_min + C_L^2 / (pi * e * A), where C_D_min is drag at zero lift, e is Oswald's efficiency factor, and A is aspect ratio of the wings.  In level flight, L = W = weight = m * g = C_L * Z.  Overall, a = T / m - C_D_min * Z / m - m * g^2 / (Z * pi * e * A).

So, in level flight, a is highly negatively impacted by m.  Not only do you have the T/m term, but m * g^2 / (Z * pi * e *A) is substantial (the contribution to drag as a result of generating lift).  C_D_min is much smaller than drag due to lift in level flight.

In a vertical dive pulling zero g's of lift, T + W - D = m * a.  Overall, a = T / m + g - C_D_min * Z / m, as lift and thus C_L is zero.  Here, T/m is negatively impacted by m, but at all speeds for WWII aircraft, and especially at speeds above near zero, T/W is much less than 1.  So T/m is much less than g.  C_D_min * Z / m is reduced as m gets larger, so the negative contribution from parasitic drag is lessened by larger mass.

Assuming that I haven't made any math errors (which is certainly possible), general trends from above:  all else equal, a heavier plane accelerates more poorly in level flight (no surprise there) but accelerates better in a vertical dive (at least when starting at a high enough speed) compared to a lighter version.

[Saxman]

Assuming that I haven't made any math errors (which is certainly possible), general trends from above:  all else equal, a heavier plane accelerates more poorly in level flight (no surprise there) but accelerates better in a vertical dive (at least when starting at a high enough speed) compared to a lighter version.

The math made my head hurt, but the end results are certainly borne out in game. As I noted before, the heavy Corsair and Hellcat certainly don't accelerate remarkably well in level flight (excluding the -4*), but point them at the ground and there's not a lot of opponents that can run on them or catch them in a dive.

* = There certainly seems to be an effect of the propeller that I don't see you accounting for, unless it's covered in the unintelligible (to me) stream of equations. For example: The F4U-4 is no lighter than the other Corsairs and its HP advantage over the other marks isn't really that significant, but it sure as hell accelerates and climbs a LOT better (not to mention the top level speed boost). The MAJOR difference is that four-bladed paddle prop. Or for a simpler example: The F4U-1A has improved level acceleration and climb over the F4U-1 despite the same engine output, loaded weight, and a marginal drag increase from the raised cockpit (the stall spoiler also added a small amount of drag on the starboard wing). The F4U-1 had the early toothpick prop, while our 1A is modeled with the later paddle-type.

[DaveBB]

Anecdotal, but Gregory Boyington was shot down in a dive in his F4U by a Zero pursuing him.

[morfiend]

Anecdotal, but Gregory Boyington was shot down in a dive in his F4U by a Zero pursuing him.

  Ya you might out dive the zero but I doubt you can out dive a bullet!



   

[Tank-Ace]

I never understood this thinking... When you have (or worse don't) altitude, diving only gives you so much time to get separation. And then the guy runs you down. Now the K-4 will climb, right to 19,000ft wep up and run you until your 100+ miles behind enemy lines if he needs to. Diving IMHO is just as valuable as roll rate. Ya it's good, but it won't keep you alive.

I've rarely had issues diving away in a 109. Unless I've got a big horde on my 6 o'clock, and they're all just spraying, D600 is usually enough separation that I can just motor away. Few exceptions being the La-7, F4U-4, and Tempest.

Besides escaping, diving evens out energy stats pretty well. And in the case of the K4, it also puts you ahead of your opponent in terms of climb and acceleration with almost absolute certainty, and puts you right up near the head of the pack for speed.

[Brooke]

* = There certainly seems to be an effect of the propeller that I don't see you accounting for

I didn't give any detail on that, but T is affected a lot by the propeller.  T = eta * 375 * gamma * BHP / v, where eta is propeller efficiency, gamma is how much of full power is being applied (0 = none, 1 = full BHP), BHP = horsepower of engine, and v is aircraft velocity.

And of course BHP matters a lot.

[save]

The P47's don't compress like the 109 does at about 450 MPH.
The P47's have better stability and handling at higher speeds.
The P47's also are more resistant to parts shredding off in high speed dives.

In theory the P47 is technically better than the K4.

The FW190A8/F8 don't compress like the P47s
FW190A8/F8 has better stability at 550mph+ than the P47s
FW190A8/F8 take at least as many bullets as a P47, and is also a much smaller target.

However a 190a8/f8 does not stand a chance 1vs1 vs pretty much any plane in a knifefight, even some 4-engine buffs out-turn it at slow speed (!).

[bozon]

* = There certainly seems to be an effect of the propeller that I don't see you accounting for, unless it's covered in the unintelligible (to me) stream of equations.
...
The MAJOR difference is that four-bladed paddle prop.
...

I didn't give any detail on that, but T is affected a lot by the propeller.  T = eta * 375 * gamma * BHP / v, where eta is propeller efficiency, gamma is how much of full power is being applied (0 = none, 1 = full BHP), BHP = horsepower of engine, and v is aircraft velocity.

The prop makes things much more complicated in a high speed dive. Paddle blade prop were much more efficient then the toothpick ones at low speeds and (at least in the case of the P-47s) increased climb and acceleration tremendously. However, they were less efficient at high speeds which reduced the low altitude top speed by a couple mph. Altitude factors in because at high alt the IAS which is the speed relevant to lift provided by a wing (fixed or rotating) is quite low. Most P-47 pilots considered this a very good trade off.

At high enough speed the prop starts to act as a speed break and instead of pushing the air through it, the wind is trying to rotate the prop instead. The RPM of the prop is limited which means that the angle of attack much be reduced at high speeds in order not to damage the engine and prop. Pilots had to reduce the RPM when entering such dives. At a terminal speed dive the prop is a huge hindrance and for this reason jets dive so much better then prop planes and also keep their over-speed better when leveling out. I do not know enough prop theory to say what kind of a prop is better in a dive, but I suspect that a prop with minimal filling factor (not sure if this is the correct term - the fraction of disk area filled by the blades) will be less of a problem in high speed dives.

Now, if you have two planes with a similar prop, one heavier then the other, and we are at a high speed dive where the prop is a major factor in drag, then engine power is irrelevant and weight is the only factor to counter the prop drag. Perhaps this is one reason the heavy American radials were good in dives.

[Brooke]

I'm not sure the 190A is as sturdy as a P-47.  I've read lots of accounts of P-47's absorbing a lot of damage and making it back.  Of course, reading about it and a statistical analysis are two different things, but it's the best I have to go on.

190A's can be excellent in a scenario environment (against their historical adversaries and historical conditions).  190A-5's did wonderfully in "Enemy Coast Ahead" against Spit IX's, for example.







And 190D's do fine against late-war allied aircraft there, too (such as in the scenarios "The Final Battle" and "Winter Sky").  The thing that helps them is the superb handling at speed, great roll at all speeds, and very low amount of oscillation upon control movement, making shots more precise, plus lots of firepower, lots of ammo load, and good top speed vs. their historical adversaries.

[Brooke]

Thrust from prop planes drops off rapidly with velocity (like 1/v).  Jet engines are more akin to constant thrust with velocity.  Jets also tend to have lower C_D_min than prop planes.  I think these are more the reasons that jet would accelerate faster in high-speed dives than propeller planes.

I haven't done the math on it, but my intuition tells me that props do not act like brakes at higher speeds but just that thrust goes to zero and that the reason prop planes hit a terminal velocity in a vertical dive lower than Mach 1 is that shock waves off various parts of the aircraft create an enormous amount of drag, enough to keep the plane lower than Mach 1, but not because of the prop.

I seem to recall that some dive experiments were done with some prop planes with prop removed, and they still hit compressibility and stayed there.

[bozon]

I haven't done the math on it, but my intuition tells me that props do not act like brakes at higher speeds but just that thrust goes to zero and that the reason prop planes hit a terminal velocity in a vertical dive lower than Mach 1 is that shock waves off various parts of the aircraft create an enormous amount of drag, enough to keep the plane lower than Mach 1, but not because of the prop.

I seem to recall that some dive experiments were done with some prop planes with prop removed, and they still hit compressibility and stayed there.

Unless the prop is feathered it will be windmilling and that means drag and lots of it. To be effective, the rotation speed of the blade needs to be similar or faster then the air velocity through the prop disk. This is probably the reason to remove the props on the experiments that you mentioned. If I recall correctly, the dive speed record in a Spit included the prop breaking apart during the dive.

[Brooke]

Unless the prop is feathered it will be windmilling and that means drag and lots of it. To be effective, the rotation speed of the blade needs to be similar or faster then the air velocity through the prop disk. This is probably the reason to remove the props on the experiments that you mentioned. If I recall correctly, the dive speed record in a Spit included the prop breaking apart during the dive.

Again, I could be wrong and haven't done the math, but my intuition is that, if you look at tip speed at top level speed and full RPM, we'll find that tip speed in a 0.9 M dive and lower RPM wouldn't imply that the disk of the prop is acting as a brake.

I believe that the main effect of props at very high speeds is that the tips can go supersonic, making thrust go to near zero, but not significantly less than zero.

[Brooke]

Doing some quick calculations shows (if I didn't make a math mistake) that prop tips for fighters are commonly supersonic during just normal flying.

Consider a P-47 with a 13' diameter prop running at 2700/2 RPM (divided by 2 since gear ratio to prop is 0.5 for the P-47).  From v = r * domega/dt = 13'/2 * 2700 rev / 2 min * 2 * pi / 1 rev * 60 min/1 hr * 1 mile / 5280 ft = 626 mph, which is the speed of the prop tip when the plane is sitting still.  When the plane is moving forward, the speed of the prop tip is sqrt(v^2 + 626^2), where v is speed of the aircraft.  It doesn't take much speed of the aircraft or much altitude to get prop-tip speed to mach 1.

At 15,000 ft., mach 1 is 721 mph, so once you hit 360 mph true, the prop tips are supersonic.

Prop efficiency goes to zero as speed of a prop plane nears mach 1, but I don't think that it goes negative.  So I don't think that the prop is acting as a brake during a high-speed dive.

[Widewing]

Prop efficiency goes to zero as speed of a prop plane nears mach 1, but I don't think that it goes negative.  So I don't think that the prop is acting as a brake during a high-speed dive.

Prop drag goes up dramatically as the prop approaches Mach 1. It becomes, in effect, a giant air brake....

[Brooke]

Prop drag goes up dramatically as the prop approaches Mach 1. It becomes, in effect, a giant air brake....

I don't think so.  I think its thrust goes to zero (or near zero), not that the prop acts like an air brake at high speeds.

A windmilling prop acts like a brake (unlike a stationary, feathered prop) because energy from the air flow is being used to rotate the engine faster than it would otherwise rotate (i.e., faster than if there were no wind).  For example, with a plane parked on the runway, chop throttle to zero and set prop RPM to RPM_max, and the prop for a lot of planes won't be spinning at RPM_max.  It will only get to RMP_max under that throttle setting if something else ads power to the rotation.

In a full-power dive to high speeds and prop RPM set to RPMx, your engine is already spinning it at RPMx, and it will maintain RPMx in the dive.  It would only act as a brake under a particular condition that I don't believe to be the case in high-speed dives, namely drag on the prop so great that the full HP of the engine can't spin the prop at that speed by itself.  I doubt that's the case for 1500 to 2000 HP engines even if much of the blade length is supersonic.

I could go through calculations on that (working to figure out the drag on the blades at, say, 0.85 M, and seeing if 1500 HP can't still spin it).  That seems like a lot of work, so I'll ponder if there is a simpler way to show it.