How to regain lost E? (F4U)

[Midway]

bozon - I agree with most of what you said.  Two points I would make:

1) P_s = (T-D)*V/W = rate_of_climb + rate_of_flight_path_velocity_ change.  Yes, P_s is not a direct measure of zoom height.  However it includes a direct measure of rate of change of climb, thus the time average of P_s over the course of a zoom climb tells you which airplane is going to zoom higher.

2) Mass absolutely is a factor which is why this topic totally throws people.  The question is how much and when.  Typically the portion of a zoom climb where T<D is very short in duration thus extra mass quickly becomes a detriment.  In the links I've posted above I've done some examples to demonstrate this (numerical integration over the time domain).  The fact that (for our prop aircraft) T increases with decreasing velocity while D decreases with decreasing velocity further ensures that T<D is only over a short duration.

  

 

[dtango]

 

 

 , it all makes a lot more sense after a few stiff drinks.  Why do you think hitech likes scotch so much .

[2bighorn]

Ah, my good sir but P_s absolutely takes momentum into account.  The derivation of P_s comes directly from F=ma.  The right-side m*a is the rate of change of momentum. Momentum is completely factored in.

The formula used to derive graph you posted is:

In this case, it illustrates the relation between P_s weight and speed. That's all. It has no other use.  Also initial delta E is not accounted for.

The point being is that Stoney and you hang up on the premise that reaching certain altitude (up to power deficit) the heavier aircraft will need more energy. This is correct.

But not many in game really care about zoom climb performance from 1k to lets say 15k alt. Most care about zoom of 3-4k from starting alt at most.

With initial E advantage of heavier aircraft, up to reasonable alt necessary to establish advantage after merge, heavies will arrive at that alt sooner (most of the times). Here, half a second advantage is all what's needed.

And hence, my reply "It is also true that, if all else is equal the heavier aircraft will zoom better" to your claim "Yes, if all else is equal the heavier aircraft will zoom worse."

Both statements are true.

[Stoney]

Specific excess power is everything in comparing performance.  Ps is used to climb, accelerate, or maneuver the aircraft, and includes the mojo that defines turn performance.  It can tell you what your best climb speed is, what your best rate of climb is, how your performance envelope compares to other aircraft.  It is a comprehensive metric for aircraft comparison, and unfortunately, to determine it accurately, its very time consuming.  If you understand Ps, you understand 80-90% of what makes airplanes do what they do.

[2bighorn]

Specific excess power is everything in comparing performance.

Definition is actually quite simple, and no, it's not even remotely close to everything in comparing performance.

includes the mojo that defines turn performance.

Not quite

It can tell you what your best climb speed is, what your best rate of climb is

It can, but it's not given.

If you understand Ps, you understand 80-90% of what makes airplanes do what they do.

  You wish

[Stoney]

You wish

Whatever bro.  You crack a copy of a flight mechanics and performance text, and it will be plastered all over the place.  But, humor me and tell me what you think we should be comparing here?  If we're wrong, what's right?

[dtango]

2bighorn...

Because it's been repeated so much I too believed that heavier a/c builds up more speed in a dive and then retains that energy better into a zoom climb vs. lighter aircraft.  Running through loads of dive/climb modeling has shown me this is completely misleading.

The question is not if increased mass makes a difference.  The question is when and how much.  I know of no other way to fully answer the question but quantitatively thru simulations via numerical integration.  Over the years, running many simulations for myself has shown me increased weight is a relatively minor factor.     

Yes, using a procrustean definition of zoom, narrowing it only to a particular moment of a zoom then at some point more mass helps.  I just think it's non-helpful to repeat the heavier a/c zooms better mantra when this only applies to a narrow band & of minimal relative significance. 

[2bighorn]

Whatever bro.  You crack a copy of a flight mechanics and performance text, and it will be plastered all over the place.  But, humor me and tell me what you think we should be comparing here?  If we're wrong, what's right?

Ever heard of gliders? No excess power whatsoever, therefore no P_s to speak of. By your account, we wouldn't know of 80-90% of what makes them fly.

2bighorn...

Because it's been repeated so much I too believed that heavier a/c builds up more speed in a dive and then retains that energy better into a zoom climb vs. lighter aircraft.  Running through loads of dive/climb modeling has shown me this is completely misleading.

The question is not if increased mass makes a difference.  The question is when and how much.  I know of no other way to fully answer the question but quantitatively thru simulations via numerical integration.  Over the years, running many simulations for myself has shown me increased weight is a relatively minor factor.     

Yes, using a procrustean definition of zoom, narrowing it only to a particular moment of a zoom then at some point more mass helps.  I just think it's non-helpful to repeat the heavier a/c zooms better mantra when this only applies to a narrow band & of minimal relative significance. 

Lets just say we shouldn't generalize. But otherwise, I agree with you.

[FLS]

Gravity is proportional to mass.

[PuppetZ]

Gravity is proportional to mass.

so is inertia. they counter-balance through a direct relation. A heavier object does not fall faster nor does it accelerate faster. At least not because of gravity. The terminal velocity might be higher or lower when you factor in drag.

[PuppetZ]

Ever heard of gliders? No excess power whatsoever, therefore no P_s to speak of. By your account, we wouldn't know of 80-90% of what makes them fly

Gliders are usually very light in relation with their wing surface so they generate plenty of lift. And gliders usually falls. You are able to climb in them but it requires some specific atmospheric conditions to happen. Namely updraft. And then it's a little like powered flight, only with a "wind" engine. I've been in a glider 2 times in my life(Canadian air cadet ones), and both time once we released the tow plane, it was down from there.

[bozon]

Because it's been repeated so much I too believed that heavier a/c builds up more speed in a dive and then retains that energy better into a zoom climb vs. lighter aircraft.  Running through loads of dive/climb modeling has shown me this is completely misleading.

dtango, I fully agree with your theory, but I am not completely confident in its application to reality. There is a reason why pilots believed the P47 zoomed better than other AC that had better Ps ( though if one goes high enough, the P47 wins in Ps when the other's engine dies of hypoxia...). At the same time they ALL preferred less weight given the option, but this is not strictly with zoom ability in mind. Equal planes were never considered - it was not a P47 vs. a P47 with a ballast stone in it, but a P47 against a P51, or a 109. If the planes have only a small difference in power loading, the kinematic part (weight and drag) play a larger role.

One reason for advantage of heavier aircrafts is that pilots were more worried about the initial part of the zoom. The threat range for gunfire was quite short and gaining a few 10s of feet DURING the zoom could be enough to get them out/in of the threat. Higher mass gives an advantage in the early zoom when starting from high speed. The last part of the zoom is where power loading dominates and where the planes are flopping about, left them too little control to make a shot - I doubt many pilots of high torque planes will be keen on kicking the rudder to align the shot, while on the verge of a stall with the nose pointed straight up.

The second related possible consideration is that we integrate the zoom too long. Most of the advantage of a light plane with (just a little!) better Ps comes in the last stages of the zoom, when it is crawling up close to the stall. We assume that the pilot will keep his noise pointed up, full throttle and fight the plane till its starts falling backward. I seriously believe that most pilots will not go as far as this and terminate the zoom much earlier. Doing a tail slide is one thing, doing a tail slide at full power... that sounds a bit dangerous and likely end up in a spin. We hear many reports of planes that were hard to control at a steep angle, full power climb. It was supposedly one of the defense moves of the P-38 to go into a steep spiral climb to the right so high torque 109/190 will not be able to follow and eventually flip over to the left. I do not know if this is really true, but this is the anecdote.

[FLS]

so is inertia. they counter-balance through a direct relation. A heavier object does not fall faster nor does it accelerate faster. At least not because of gravity. The terminal velocity might be higher or lower when you factor in drag.

A heavier aircraft falls the same speed as a lighter one in a vacuum. In atmosphere a heavier aircraft gains more thrust from gravity than a similar lighter aircraft. This is why more weight makes a sailplane fly faster but doesn't change it's glide ratio.

Since gravity has a vector the heavier aircraft only benefits from it's weight when  descending or flying level. As soon as you nose up to zoom the heavier aircraft is at a disadvantage.

[PuppetZ]

A heavier aircraft falls the same speed as a lighter one in a vacuum. In atmosphere a heavier aircraft gains more thrust from gravity than a similar lighter aircraft.

Gravity's acceleration is constant regardless of the mass of the object. On earth it's 9.2m/s. Up to terminal velocity which is affected by the drag imposed by the shape of the specific object. As planes have roughly the same shape, they accelerate at about the same rate at first until they reach a point where drag dictate the final velocity of the fall. If what you said were true, heavier object would fall faster on earth(which has already been proved wrong by experiment). Similarly shaped object will acheive a very close terminal velocity, determined solely by the amount of drag they generate. A steel ball does not fall faster than a wooden one of the same size, even with a big mass differential. Now planes are not inert object, and they usually fly powered so their straight down acceleration rate will be (9.2m/s(gravity constant) + whatever the engine add minus drag). That makes a big difference. And it comes down again to thrust/weight ratio. Why? To answer that, we have to define what is acceleration. Acceleration is a change of velocity along a vector. To change the velocity, you have to apply enough force to overcome inertia. To apply it to powered flight, acceleration is proportionnal to the ability of the engine to overcome the inertia of the mass of the plane(and drag, that's why the faster you go the slower you accelerate. think about the time between 0-100 vs 200-300). Now to understand how this act, we must go back to the basic 4 forces that act on a plane : gravity, lift, thrust, and drag. When flying level, gravity is balanced by lift. When in a climb, some of the engine power is used to fight gravity and the extra lift is used to climb. Now if a plane point straight up, gravity sole opposite force is thrust as the lift vector now point parallel to the horizon. Deceleration rate is a function of (gravity constant - engine thrust - drag). A higher thrust/weight ratio will let you acheive a higher altitude. When thrust/weight ratio exceed 1:1, we have a craft that will accelerate pointing straight up, like a rocket on the launch pad or the space shuttle. Weight is not an advantage nor is it a disadvantage as long as you got a big enough engine to get you moving. A lot of factor come into play but it boils down to the aformentionned 4 forces. 3 of them are dynamic, 1 is not. You cannot change the laws of physics.

Now the question about how this is all modeled in the game is a completely different beast. But with what i've already seen iof the game, I'm sure HTC are already aware of all this.

[Stoney]

When thrust/weight ratio exceed 1:1, we have a craft that will accelerate pointing straight up, like a rocket on the launch pad or the space shuttle. Weight is not an advantage nor is it a disadvantage as long as you got a big enough engine to get you moving. A lot of factor come into play but it boils down to the aformentionned 4 forces. 3 of them are dynamic, 1 is not. You cannot change the laws of physics.

But with our aircraft in this game, none of them have a thrust to weight ratio that gets even close to 1:1 even in full WEP.  Thrust to weight ratio isn't a good metric to use with prop aircraft anyway--that's more of a jet thing.  Power to weight ratio is the metric used to characterize propeller aircraft, and to compute power, you have to account for the BHP at whatever altitude and propeller efficiency. 

Anyway, weight will always be a limiting performance factor with the planes we have in-game.  Every plane in this game will suffer a performance penalty when their weight is increased, and this applies to zoom climbs, turns, whatever...