Calculating aircraft performance

[Pinin]

EI have data of a Dornier Wal floatplane with BMW VI engine(x2) 600hp and would want to calculate it with Hispano Suiza Ydrs of 860hp

This is the data for BMW VI version 600(650hp?)hp x2 Dry weight: 510 kg (1,124 lb) Displacement: 46.93 L (2,864 cu in)
BMW VI - Wikipedia, the free encyclopedia


Empty weight: 4000kg
Crew: 510kg(6 crew)
Lubrificant: 100kg
Fuel:1100kg
Armament:2x2 Darne with 12 box ammo(200 rounds per box): ~100-150kg
Various: ~200kg(radio, etc)
All up weight around 6450 with bombs.

Performance : 216 kph max speed, 176 kph cruise speed.
Climb: 125m/min 16m09sec to 2000m, 42m 8sec to 5000m - this goes against the data that ceiling is only 4600m.
Range 800km to 1300km


With RR Eagle IX engines 355hp x2 Dry weight: 900 lb (408 kg) Fuel consumption: 24 gallons per hour (90 Litres per hour), Displacement: 1,239 in³ (20.32 L) Rolls-Royce Eagle - Wikipedia, the free encyclopedia

Maximum speed: 185 km/h (115 mph; 100 kn)
Cruising speed: 145 km/h (90 mph; 78 kn)
Range: 800 km (497 mi; 432 nmi)
Service ceiling: 3,500 m (11,483 ft)
Rate of climb: 1.5 m/s (300 ft/min)
Time to altitude: 3,000 m (9,843 ft) in 33 minutes


Data for Hispano Suiza Ydrs Hispano-Suiza 12Y — Wikipédia
860hp at 4000m, 460 kg Displacement: 36 Lit.

It is clear aero is not the strong in this floatplane, and increase of 710hp to ~1200hp(69%) only improved speed 30kph(16%) so an increase in power from 1200 to 1920 of 60% should only give probably 20kph more: increasing drag will blunt even more the power increase that is even less proportionaly: 60% instead of 69%.

If speed is relatively straightforward the rest is more complicated due to lack of data.
With Hispanos a lighter engine than BMW's and more power it is clear that aircraft should be much more capable in climb and ceiling
With BMW's the power loading is 0.186 hp per kg. With Hispano and same max weight(6450kg since the engines are even lighter there is even cargo capability* ) we have a 0.297hp/per kg.
We can increase max weight up to 10300kg to return to same power loading of BMW tough this is not without penalty since in another hand the wing loading increases much.

*It is probably to be expected that due to increase in power the fuel needs and lubricant oil increase with Hispano which in turn means bigger fuel and oil tanks. This would certainly offset the weight saving from 460kg engines instead of 510kg engines.

Assuming same comsumption per horse power at 800km range with 1200hp we would have 500km range with 1920hp for same fuel quantity same proportional power settings - this would mean that 1100kg fuel would need to be 1760kg instead to achieve 800km. This is 660kg weight more in maximum weight. pushing the aircraft to around 7100kg
which still doesn't deny the power loading Hispano advantage that we see is only achieved at 10300kg

Of course this is pretty much fuzzy and worst case scenario since the BMW VI power and cruise is not known at what altitude it is, if it is at low level then the Hispano might be much more economical at 4000m altitude since drag resistance is minor instead of being equal per horse power like in this calculations.

Any ideas and/or mistakes noticed?

 

[Zipper730]

I'm not sure, but I think this is a thread that has promise

 

[Shortround6]

Some things about aircraft performance are actually counter intuitive.
Like you can actually improve the rate of climb by cutting the wing area.
Climb rate is governed by the amount of surplus power you have after you take into account the power used to fly at best climb speed (varies by aircraft) and since the lift of the wing is proportional to the square of the speed doubling the speed from an 80mph stall to 160mph climb (or lowest drag in level flight speed ) gives four times the lifting power. I am not saying this quite right.
Here is a drag diagram.

At low speed the wing has high induced drag due to the angle of attack needed to generate needed lift. As speed increases the wing can generate the needed lift with much less angle of attack and much less drag. Climb is the excess power applied to the increased drag of increasing the angle of attack of the wing more than is needed in level flight. A 15-25% smaller wing on some planes may result in better climb because of less form drag even at a slightly higher speed.
Remember lift goes up with the square of the speed. Drag goes up with the cube of the speed.
Our 80mph to 160mph example has 4 times the lift at 160mph but in form drag 8 times the drag. Cutting drag, up to a point, will compensate for the less lift.

 

[swampyankee]

To a first approximation (you know this), speed will increase by the cube root of the engine power, so doubling power will only result in a 20% or so increase in speed. It will also result in a substantial decrease in range unless fuel supply is proportionately increased. Obviously, increasing power won't decrease power-off stall speed, Acceleration and rate of climb will be improved.

There are some fairly good textbooks out their, such as Raymer's series on design, that can give you far more information.

 

[Shortround6]

Something to be aware of is that they changed the way they rated engines between the 1920 and the 30s.
That and improved fuels often changed the short term power level (take-off or military as they would be known later) but didn't change the Cruise ratings much.
For instance while the P & W Wasp (R-1340) was introduced at 410hp and quickly went to 450hp with a larger crankpin. But the 450hp was not only the take-off rating, it was also the max continuous rating. In those days of fixed pitch props and 73 octane (or less fuel) the pilots could with many engines (there were some exceptions) run them at full throttle for as long they wanted, engine temperature and fuel permitting. The jumps to 500-600hp came with higher octane fuel (more cylinder compression, more boost) and more RPM.
However a late model (600hp) R-1340 could cruise at 400hp at 2000rpm compared to a 1930 R-1340 being able make 420hp at 2000-2100rpm and do it for hours.
Climb in a flying boat like the Wal could take 15-20 minutes to reach a cruising altitude even a bit below 10,000ft. as noted with the Rolls-Royce engines. While climb with Hispanos would be better climb would not be done at the 860hp rating.

 

[Zipper730]

Something to be aware of is that they changed the way they rated engines between the 1920 and the 30s.

Now that's something to know!

 

[GregP]

Stall speeed increases as the square root of the new weight squared divided by the old weight squared. 6450 kg is about 14215 lbs. Suppose the new engine is 100 lbs heavier and you add 250 lbs more fuel, the new weight is 14565 and the stall speed goes up by about 2.5%. So if your old stall speed was 50 mph (80 kph), the new stall speed would be 51.2 mph (82.4 kph).

Simplistic, but a good approximation.