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# Cruise speed of propeller-driven aircraft

## Question

I built a small plane powered by electric ducted fans and a few RTGs, which is capable of infinite flight. I was flying it on long flights around Kerbin where I set MechJeb to cruise at 4000 m altitude. I noticed something interesting, which is that the maximum cruise speed decreases as latitude increases. At the equator, it could cruise at 280 m/s but this speed gradually drops to 250 m/s at 60° latitude, which is a difference of more than 10%. As I flew back towards the equator, it gradually increased back up to 280 m/s. Even more interestingly, the blade pitch at which this maximum cruise speed occurs decreases from 49° at the equator to 46° at 60° latitude.

The electric motors are always at constant (maximum) RPM and the mass of the aircraft is strictly constant as no fuel is involved at all. This is not an issue of bad controls as the plane is just not physically capable of cruising at 280 m/s at 60° latitude.

I think the reason has to do with the temperature, pressure and density of air varying with latitude. Can anyone explain?

Edited by VincentThacker

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The lower speed of sound in colder air explains some of the lower aircraft speed.

The drag of the fan blades goes up significantly, and their lift falls, as the speed of the blades through the air increases through the speed of sound.  That means propeller-driven craft have a top speed somewhat under the speed of sound, as the blades are moving through air faster than the craft.

I don't think it gets cold enough to make a 10% difference, though.  Maybe KSP also has the density fall more quickly with altitude, over the colder regions of Kerbin.   If you still have quick-saves at different latitudes, you can use the alt-F12 debug menu =>Physics=>Aero=> display Aero GUI to see the temperature and density of air around the craft, to see which properties vary.

The fan blade gives the most thrust when it meets the air at 5° angle of attack, so the optimum blade pitch will be flatter at lower speeds.

Edited by OHara
Turns out the temperature difference is big enough. 306 K (33°C) and 351 m/s at the equator; 253 K (−20°C) and 319 m/s at 60°. I'm glad we have the Gulf Stream keeping us warm.
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It is due to the drop in the speed of sound.  The temp difference is enough to cause this issue.

Remember, your total blade apparent speed is a vector sum of the craft forward motion, and the blade rotational motion.

To decrease blade apparent speed by, say, 20 m/s (the approx drop in speed of sound going from 4km at the equator to 4km at lat 60) requires 1 of 2 things:

1. A decrease in forward velocity of greater than 20 m/s. (Your case)
Or,
2. A decrease in forward velocity of 20 m/s and a reduction in blade rotational speed via reduced rpm.

Basically, as speed of sound changes, ideal blade rpm must change. Which is why at high altitudes on Duna for example, you get better performance running your blades in the mid 300's rather than 460 rpm.

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I'm not the greatest expert in plane aerodinamics, but I can suggest checking if the rotor is still working at top speed (460 rounds per minute). When the air becomes more dense, the propellers face more drag, and as a result to rotor may not be able to push it at full speed anymore.

also, sometimes propellers can get bent; i've seen it happening in particular when you leave the propellers active in vacuum, or when you reload with the propellers moving in a thick atmosphere. If thet get out of shape, they will lose efficiency.

if neither of those is the reason, then yes, it's up to air density and pressure. I'm not sure on how those impact the efficiency of propellers, but I know they do

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3 minutes ago, king of nowhere said:

I'm not the greatest expert in plane aerodinamics, but I can suggest checking if the rotor is still working at top speed (460 rounds per minute). When the air becomes more dense, the propellers face more drag, and as a result to rotor may not be able to push it at full speed anymore.

also, sometimes propellers can get bent; i've seen it happening in particular when you leave the propellers active in vacuum, or when you reload with the propellers moving in a thick atmosphere. If thet get out of shape, they will lose efficiency.

if neither of those is the reason, then yes, it's up to air density and pressure. I'm not sure on how those impact the efficiency of propellers, but I know they do

Thanks for your reply. Yes, I have mentioned in my question that the propeller is always at maximum RPM of 460.

Edited by VincentThacker
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1 hour ago, OHara said:

I don't think it gets cold enough to make a 10% difference, though.

I agree, the temperature difference doesn’t appear to be enough to generate the effect observed.  I have also noticed this, in my case I was operating a turbo-prop powered boat.  So I was at sea-level, not 4,000 m.  But I also noticed the significant decrease in performance at high latitudes.  My first guess was also temperature changes, and the resulting change to the speed of sound.
However, I think there may be something additional going on.  I’m just not sure what that could be.

Edit- I just remembered I have also seen this with jet-powered boats on Kerbin.  Again, this would be at sea-level.  The boats I was testing used either the Wheelsey engine or the Goliath (giant jet engine).  Those vessels also exhibited the same decrease in performance at high latitudes- either a significant drop in top speed, or a significant increase in fuel flow to maintain a given speed.

Edit #2-  One guess I have is the way KSP calculates surface speed.  Perhaps there is a rounding error occurring at high latitudes?  I think I have a way to test this theory, but won’t be able to do it today.

Edited by 18Watt
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Another factor is centripetal force. At 60 degrees latitude your bonus velocity from Kerbin's rotation is halved so your centripetal force is reduced. This means you need more lift to stay in level flight, which means more drag, which means lower speed.

Edited by camacju
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On 8/31/2021 at 1:00 PM, camacju said:

Another factor is centripetal force. At 60 degrees latitude your bonus velocity from Kerbin's rotation is halved so your centripetal force is reduced. This means you need more lift to stay in level flight, which means more drag, which means lower speed.

That occurred to me, too. However, if you run the numbers based on Kerbin's radius and rotation speed, centripetal acceleration turns out to be only about 5 cm/s2 at the equator, or 0.5% of gravity. So that seems way too negligible to produce as dramatic a variation as OP was observing.

(Plus, if that were the case, he'd notice a big difference at the equator depending on whether he's flying east or west, and he didn't mention anything about that.)

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deleted

Edited by Zacspace
Not an answer. Wasn't paying attention to what part of the forum I'm in.

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