OK guys, I don't have a lot of time to explain so I'm going to be brief. I'm headed to Central Texas for the long weekend and playing aero babysitter isn't anywhere near the top of my list of things to do so
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1) Specific Excess Power (Ps)Ps gives us a measure of the energy rate of change for an aircraft. Want more info on it you can dig it up from this thread among other places:
http://bbs.hitechcreations.com/smf/index.php/topic,209163.msg2488778.html#msg2488778The general equation for it is:
Ps = (T - D) * V / W = dh/dt + (V/g)*dV/dt
Honestly I have no idea how you guys can magically estimate what an aircraft's "energy retention" should be in your head without working through what the value of Ps in every situation and flight condition. For a constant speed climb at least it's easier to calculate but for a zoom I have to resort to numerical methods to solve it to have even a clue because being a mere mortal I can't do the math in my head with the number of variables and non-linearity involved. You guys are gods to do all that ciphering in your head! I bow down, unworthy.
To show that E retention is wrong you have to show where the Ps relationship has been violated.
2) F4F vs. B-239This one is a little easier to explain because we can use the steady climb charts to demonstrate.
As you can see the B-239 pretty much outclimbs the F4F across the envelope in a steady climb. In a steady climb dV/dt=0 therefore our Ps equation resolves to:
Ps = (T - D) * V / W = dh/dt where dh/dt is the rate of climb
As alluded to by Stoney specific excess power tells us about the amount that T>D which can be used for accleration or steady climb. Because the F4F W > B-239 W we can safely assume that the B-239 will probably also out zoom an F4F just as the RoC difference indicate for steady climb.
3) Well what about the P-47's you say?That's a little more complicated. Firstly let's just plot out a couple of RoC charts.
First thing to notice, without WEP the P-47 D11,25,40's are outclimbed by the B-239 roughly below 5k at Military Power. But at WEP for the most part the D11 (marginally except below 5k), D25 & D40 all have better RoC's. So there must be something wrong with the B-239 then right??? Not so fast.
a) the speeds that you're comparing the climbs matter. The charts above are at best RoC for each aircraft and they are different. If the P-47 however is climbing in a steady climb but at a lower speed than it's best climb speed then it's RoC will get worse because of greater induced drag.
b) this is different than the F4F vs. B-239 case because the P-47 is much heavier bird than the B-239 so you have to understand what the impact of that's going to be in an accelerated zoom climb. The forces in the direction of travel in a zoom climb resolve to:
F = ma = T - D - W*sine(climb_angle)
At steady climbs climb_angle is small therefore the impact weight is lower. However where climb_angle increases the impact of weight increases. In a zoom climb the climb_angle is pretty high which means weight has much more of a detrimental impact on zoom climb peformance. So it's totally conceivable that the B-239 could zoom better than the P-47 D11, D25, & D40. Again I have no idea how you guys can factor all that in your head to know what the impact is for sure. To figure out how the above relationship varies I have to resort to numerical methods for resolving integration of partial differential equations to even estimate it.
4) But doesn't greater weight mean more mass which means heavier things retain energy better?This is a partial truth which is wrongly applied to aircraft. Where airplanes are concerned increased weight overall reduces zoom climb performance. See mace and my posts in this thread for an explanation of this fact (Stoney - thanks for pointing the thread out):
http://bbs.hitechcreations.com/smf/index.php/topic,266321.msg3328531.html#msg3328531Bear in mind that I'm only assuming 1g load factor in all the above. In n>1 Apples to apples this would generally make it even worse for the heavier plane. Bottom line for me: Could there be something wrong? Yes. However maybe folks should start asking why what you observe is actually RIGHT instead and look for the explanations for why it's right instead of assuming it's wrong.