Maximum speed as a function of temperature

[Nobody Special]

I noticed a significant difference in behavior between playing Georgia at War and Syria at War, so I did some simple testing.

 

I set up an F-14B with full fuel and no external loadout, at 25000' MSL and 950 knots which is approximately M1.5. Fly to the necessary altitude, then set autopilot on to heading and altitude hold, maintain maximum dry thrust. Accelerate time, wait for everything to stabilize and note the final IAS. I tested this at nominal (mission editor MSL) altitude and instrumental altitude but that didn't make much difference.

 

At temperature -10C I can sustain M1.7 / 750KIAS; at 0C this is reduced to M1.6 / 720KIAS. At 10C M1.53 / 690KIAS or so. At 20C it's M1.44 / 650KIAS. But at 35C the plane decelerates to M1.04 / 450KIAS. I'm not claiming there is any problem, just thought this was interesting. It is a dramatic difference in performance in hot weather. I'm not sure if this is solely a difference in engine performance, or if the density of air is different under these testing conditions.

Edited May 23, 2021 by Nobody Special
Corrected numbers, the mission editor sometimes changes the input temperature

[Victory205]

A higher temperature requires a higher speed to reach a given Mach number.

 

Mach varies directly proportional to temperature. The warmer the air, the higher the speed of sound. On a standard day, the speed of sound at SL (15C) is 661 knots, at 36,000, the notional height of the tropopause (-56C), Mach one is 573 KTAS. In your example, you increased the temperature dramatically at altitude, making the speed of sound much faster, reducing the ratio of actual velocity relative to the speed of sound. Mach is a ratio.

[Nobody Special]

Thanks @Victory205 - I'm aware that the speed of sound depends on temperature and pressure. But I'm not sure temperature alone explains these data; the effect is dramatic, and IAS changes similarly. I didn't expect that.

 

From thermodynamics the speed of sound should vary as the square-root of temperature. A 45C increase from 263K should result in ~8% change (from Vs = 331 sqrt(T/273) m/s, valid at sea level but the proportion should not depend on density). But what I found is a ~35% change in both Mach and IAS. Not trying to do a "gotcha" here - there are other factors, the most obvious being engine performance. I think that pressure is kept constant by using constant indicated altitude (?).

 

Here is the reason I'm interested in this: when facing overwhelming numbers of bandits, my tactic has been to turn cold once I'm Winchester and/or distance has closed to ~20 miles.  I'll use AB as needed to reach supersonic speeds, then drop to full mil power to conserve fuel. In Georgia at War, this often results in ~M1.45 or so - fast enough to keep a Flanker in afterburner from catching me. The trick is, since bandits have to use AB and I'm sipping fuel (relatively speaking), eventually they'll run low of fuel and RTB. I'm not sure if the same tactics will work in Syria at War. I'm trying to understand if my (ground) speed really is dramatically lower, or if this is just an instrument effect. I understand that the flight model fidelity may vary between different aircraft (never mind the fact that AI planes can be UFO's) -- I just want to understand the F-14's performance.

 

I just found a useful calculator here. Using that to modify the temperature appropriately, I see that CAS and Mach actually do not change, but TAS does. That is consistent with my observations, and it suggests the F-14 top speed really does decrease by about 35% in hot weather. Interestingly, this also roughly confirms my estimate of the real impact of temperature on Mach: at fixed TAS, changing temperature by 45 degrees results in a ~10% change in Mach number.

[Victory205]

Density altitude is pressure altitude corrected for non-standard temperature. The short answer, is that it affects lift, including within the engine, which reduces thrust. I am not typing up the formulae. Think of the effect of temperature on takeoff performance of a jet, even at a constant pressure at sea level. 

 

Grab yourself a copy of Aerodynamics for Naval Aviators. It’s all over the net in pdf form. Lots of information there, starting on page 2.

[Lurker]

35 degrees C, at 25 thousand feet. Hmmm, Not sure that would even be possible on this planet

[Victory205]

If you pay attention to the Climate Change Doomers, not only is it possible, it’s inevitable…we’re always ten years from complete, utter disaster.

 

It’s going to require longer runways and longer wings, that’s for sure.

Edited May 24, 2021 by Victory205

[RaisedByWolves]

44 minutes ago, Victory205 said:

If you pay attention to the Climate Change Doomers, not only is it possible, it’s inevitable…we’re always ten years from complete, utter disaster.

 

It’s going to require longer runways and longer wings, that’s for sure.

 

Hahaha. 

[Nobody Special]

The temperature is not 35C at 25000'. I believe that is the surface temperature.

 

Grabbed the PDF and I'm reading.

[Victory205]

Lots of interesting information in the publication concerning turbojet performance considerations, high speed flight dynamics, including Mach effects, stability, etc. We used it as a base document for advanced strike aerodynamics. Everyone should have a copy sitting on their shelf. 

[Nobody Special]

For comparison, I ran the same test with the F-18, getting as close as I could to 100% RPM without afterburner. The result is similar overall but a bit less in magnitude:

At 0C, 25000' maximum HUD indicated speed 580

At 35C, 25000' maximum HUD indicated speed 418

 

That's essentially the same loss of speed that I see with the F-14B, to within my ability to measure: the ratio (speed at 0C) / (speed at 35C) is 0.72; for the F-14 that ratio is about 0.69. So my tactic of out-running the enemy ought to be okay so long as they obey the same laws of physics that I do.

 

I had no idea that the effect of temperature on turbine performance is so large. Good to know!