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With a 30 or 40 knot head wind that 4570 fpm is going to be a lot higher.
It probably was a lot lighter - your calcualtions are based at over 10,000 pounds. Do the same calculations with 50 gallons of fuelF8F-2 weight 10,400 lbs = 4,727 kg
Force required to lift 4,727 kg at 9.8g = 46,325 n
Energy required to get to 3,048m = 141,198,600 j
Power required to do it in 94 seconds = 1502113 w
1502 kw = 2,014 hp
That assumes the plane is already flying at climbing speed. As it was stationary, we also have to work out the power required to accelerate up to climbing speed.
Assuming best climb is at 160 mph, but that wind speed is 40 mph, the plane has to accelerate to 120 mph.
Power required to accelerate from 0 to 190 km/h = 70 kw, 94 hp
So power required is an average of 2,108 hp over the 94 seconds.
However, that ignores several things. Firstly, prop efficiency. A WW2 propeller is typically about 80% efficient. So the engine needs to be producing about 2,630 hp
Finally, you have to account for drag. The plane needs an air speed of about 160 mph. Drag (including induced drag) will be quite high. The plane needs 2,630 hp excess hp, ie 2,630hp more than the power required to maintain level flight at 160 mph.
Unless I've made mistakes in the physics (which is entirely possible), the F8F needed to be either a lot lighter, or have a lot more more power than normal, to reach 10,000 ft in 94 seconds.
The headwind will make no difference to the climb rate.
The only effects will be to make the ground distance covered during the climb smaller, and to reduce the speed the aircraft has to accelerate to from a standstill (ie a plane stationary on the runway in a 40mph headwind already has an indicated air speed of 40 mph)
I have flown aircraft where I normally see 500 - 800 fpm. Add a 20 or 30 knot head wind and I see 800 - 1000 fpm (or more), all at the same Vx.
Temporary or sustained ?
Im with Hop in this. Headwind/downwind does not affect sustained climb rate.
Temporary - wind gradients change as does other aspects of the weather. As stated normally see 500 - 800 fpm. Add a 20 or 30 knot head wind and I see 800 - 1000 fpm (or more), all at the same Vx.
From the story it seems that the 2 pilots had practiced this several times before the try for the record at the air races. They probably had the fuel load worked out and there may have been a bit of fudging about the ammo load. I don't know about 1946 but earlier the navy seemed to have at least 2 ammo loads for some of it's fighters, "standard" and "overload" with 'standard' being around 200rpg and "overload" the full capacity of the ammo boxes.
The most important piece of data we are missing is what the actual power level was on that day. The engines were fitted for water injection and the power level with water injection is hard to come by, we also don't know if the pilots in question were using a couple of "extra" inches of MAP for these flights. From Krieghund's posts it seems the "official" rating of the F8F-1 was 2380hp for take off and 2400hp at 1000ft in "combat" or wet mode. Power in low gear was falling off the higher it went but is there a possibility that they could shift into high gear lower than normal?
When you say "glide slope" I'm assuming you're actually meaining "glide ratio" - the ratio of the distance forward to downward. In a headwind you will have lift being generated over the wing, again "excess thrust." That excess thrust will allow you to increase angle of attack and thus increase life and in the end gain altitude IF SUSTAINED.I could be way off with this idea. What happens with gliders?
No power (or power off) is there a difference in the glide slope from no wind to head and/or tail wind. Distance over ground will certainly change for the same loss in altitude but does the actual glide slope change at all?
And surface temperature needs to be calculated as well.Even the F8F manual does not give the "wet" (water-methanol -injection) -rating of the engine. I have seen figures of 2,800 hp.
And the plane apparently was the F8F-1 model ( 9,600 lbgross, with guns and ammo, but the fuel load is not known), not the heavier F8F-2.
Cleveland (Ohio) airport is at 800 ft altitude. So was the climb actually to 10,000ft pressure height ?
When you say "glide slope" I'm assuming you're actually meaining "glide ratio" - the ratio of the distance forward to downward. In a headwind you will have lift being generated over the wing, again "excess thrust." That excess thrust will allow you to increase angle of attack and thus increase life and in the end gain altitude IF SUSTAINED.
It probably was a lot lighter - your calcualtions are based at over 10,000 pounds. Do the same calculations with 50 gallons of fuel
Think about this...
Climb performance is based on excess thrust. Excess thrust is used to create lift. If the headwind is providing you with X amount of lift, there is more excess thrust available.
This has nothing to do with ground speed. Headwind is proving you with excess thrust. Excess thrust provides lift, if angle of attack is increased thus a greater rate of climb.It's certainly possible with enough weight removed. I won't bother redoing the calculations because I have no idea of the power required to overcome drag, or any other losses.
Headwind doesn't provide lift. Once airborne, the plane is free to move with the air. To the aircraft, there is no difference between an airspeed of 160 mph in still air and 160 mph in a 40 mph headwind. The only difference is in ground speed.
Is that not the reason why a wing would lift in a wind tunnel?
That combined with a minimal fuel load, 40 knot head wind (that increased in altitude) makes this feat very "do-able." And to continue the discussion with the head wind, this is only a "temporary" advantage that was available that day that helped this feat to be accomplished.