Speed vs Altitude

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Zipper730

Chief Master Sergeant
4,430
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Nov 9, 2015
I remember a formula that stated that the speed of an aircraft all things being equal was the cube-root of the horsepower.

I'm not sure how that factors in with altitude? Is there a way to simply multiply that by the change in air-density or air-pressure to compute an estimate for altitude?
 
That formula is rough estimate for drag.

And to use it you needed to know how much power it took to fly a certain speed for that aircraft. you then figured out the cube root of the power needed. Multiply that times the desired increase in speed (say 10%) and cubed the result to get the needed power.

It takes no account of any changes in the drag coefficient as the speed changes so it works best for speeds under about mach 0.6, Some planes having a much sooner or sharper rise in drag after that point.

Changing the altitude not only changes the air density it may/will change the power of the engine.
 
Shortround6 said:
That formula is rough estimate for drag.
Click to expand...
Yeah, I'm aware of this.
And to use it you needed to know how much power it took to fly a certain speed for that aircraft.
Click to expand...
I was basically trying to figure out how much faster the XB-15 would have been able to go if it had an R-2600 in it and had either a twin-stage supercharger or a turbocharger.
 
Make up something.

Wright never successfully developed either a two stage mechanical supercharged R-2600 or one that successfully used a turbocharger.

Please note that there were two different R-2600s in the early part of WW II, with either 1600hp for take-off or 1700hp, the 1700hp version used a steel crankcase instead of aluminium among other changes.

The XB-15 used a wing with 60% more area than a B-29 and the airfoil was higher drag.

For the sake of argument let us say that Wright did develop one or both superchargers (mechanical and turbo) to the same extent P & W did with the R-2800 (while keeping the engine from melting down)
SO you get 1600hp at 25,000ft with the turbo and 1320hp at 22500ft for the mechanical two stage if applied to the 1600hp version (the first one).

Now compare to the B-17 which had 1200hp per engine to about 25,000ft.
The XB-15 wing had 96% more area. Airfoil may have been close (or identical?) but the XB-15 was so thick that crewmen could crawl out into the wings and reach the engines in flight.
Your souped up XB-15 only has about 33% more power in a much larger/ heavier aircraft using the turbo, with the two stage mechanical supercharger things are worse.

Please note that a B-17E could make 214mph at 5000ft with 650hp per engine and 250mph at 5,000ft using 1000hp per engine ( at the absurdly low weight of 40,260 lbs) compared to the XB-15 making 200mph on 850hp (?)per engine. (weight unknown?)

Cube root law says that the XB-15 needed 1633hp to hit 250mph at 5,000ft.

Compare as you see fit to B-17 results. (B-17 could get 1200hp per engine)
 
Shortround6,

So just take horsepower / mph^3 right?

XB-15 = 6400/x^3, or 5280/x^3? Was the speed figures for the XB-15 based on a specific weight?
B-17E = 40260/4800 produces a power loading of 11.92%; with the horsepower divided by cube root I get for maximum speed 4800/318^3 = 0.000149265650317

If I were to take the power to weight ratio of the XB-15 fully fueled minus 10,000 pounds of bombs (2,000 pounds of load), I'd get 60710 pounds with 5280 to 6400 horsepower and a power loading that's around 8.7 to 10.5 vs the B-17's 11.92, and that would be tantamount to the B-17 having 1061 horsepower per engine of 4244 total making for a reduction of 556 horsepower, and with the twin-stage supercharger, I'd get 3500 about making for a difference of 1244 and that correlates to 8.22 to 10.75 mph difference. The fact that I'd only be able to get to 22,500 with twin-stage would further reduce this an I'd have a top speed still over 300 mph if these numbers work out.

For obvious reasons I have suspicions
 
Which means the XB-15 will be slower than the B-17E which only needed 1000hp per engine to hit 250mph.

Power loading doesn't mean a whole lot for speed for quick and dirty calculations. the connection is that while thrust has to overcome drag (and a 2780 sq ft wing is a massive parachute) the wieght comes into play by requiring a higher angle of attack at a given speed an so changes the drag. B-17 at 41,000lbs and 250mhp has a certain angle of attack. B-17 at 54,000lbs and 250mph has a higher angle of attack (incidence) on the wing and thus has a higher drag and needs more power. The increase in angle of attack depends a bit on the airfoil so not all planes will show the same increase in drag with the same weight increase at the same speed. They may be close.

Please note the XB-15 was lacking in armor and self sealing fuel tanks and while it's suite of guns was good for 1937-38 it was pretty poor by 1941-42 standards.
 
wuzak said:
Assuming the R-2600 produced 1600hp @ 5,000ft and the R-1830 produced 850hp @ 5,000ft and teh speed of the XB-15 was 197 @ 5,000ft (from wiki), and no extra drag from engine installation, the XB-15 would have a maximum speed of ~245mph @ 5,000ft.
Click to expand...
What about 21,500 feet on 1350 hp an engine, and 25,000 on 1600 hp an engine...
 
Basically you are slower than a B-17E. You have picked up around 3000lb or more (4000lbs?) in powerplant weight (add to empty weight) of engines, propellers and so on over the XB-15 with the twin wasps. You either have to increase the gross weight or cut into the fuel or bomb load.

BTW notice the difference in surface finish/texture on the wing. The XB-15 was fabric covered from the mainspar to the rear of the wing.
 
Shortround6 said:
Basically you are slower than a B-17E.
Click to expand...
Obviously, I was just curious by exactly how much
You have picked up around 3000lb or more (4000lbs?) in powerplant weight (add to empty weight) of engines, propellers and so on over the XB-15 with the twin wasps. You either have to increase the gross weight or cut into the fuel or bomb load.
Click to expand...
So weight goes to 63710 or 64710 on the engine changes alone.

The armament seems to be
  • Forward: In the nose
  • Forward Ventral the bulge just behind the glass nose
  • Waist-gunners on either side of the rear
  • Dorsal turret
  • Ventral blister
Correct?
 
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