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Relationship between atmospheric density, gravity, and prop thrust


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Hi, I'm having fun building quad copters, I got a pretty nice one that has a 83 minute flight time, lifts 20 tons in payload, and flies well up to 3.5km on Kerbin, any higher than 5k and it stalls and crashes. 

 

Without using the cheat menu to adjust the conditions on Kerbin, I'd like to know how to figure out how well it would perform in the atmosphere of other bodies. My intuition tells me that it would fly on Eve, likely at a much greater altitude than on Kerbin, but would not fly on lathe or Duna since both have such thinner atmospheres. But I don't know enough about how atmospheric density and weight affect the thrust of the propellers to have any confidence in that assumption.

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Your assumptions are in the correct direction. 

If you want to be quantitative, get the atmospheric density and surface gravity for your destination planet. The wiki is still accurate for this kind of thing.  The props on KSP craft almost always have a maximum rotation speed independent of the atmosphere. 

The speed at which the prop moves the air is directly linked to the speed of rotation.  So, the area caught by the disk of the prop, times the speed it moves atmosphere through the prop, times the density of that atmosphere, gives the rate it is throwing mass down.  One more factor of the speed it can throw air down, gives the force generated.  The units work out (m² × m/s × kg/m³) × m/s = kg m/s² which is mass times acceleration, which is force as defined by Newton, and the resulting combination of units matches the definition of the unit 'Newtons'.

In all that, only the density of atmosphere is the only factor likely to change significantly when you take your copter to another planet, so double density means double force from your prop.

The other side of the question is how much force you need to lift the craft: its mass times the local gravity.

57 minutes ago, quazarz said:

any higher than 5k and it stalls and crashes

You might get more out of it by flattening the pitch of the prop at higher altitude . . . if you want to spend time on this kind of thing; you would also decrease the climb speed.

Edited by OHara
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@OHarasums it up nicely (like so many of OHara's posts) but I'd just throw in a couple of extra thoughts as you anticipate other atmospheres...

A prop is simply a rotating wing and when measuring the force of wings, they provide lift, but in the case of props it is thrust but otherwise similar. The actual equation for sake of my examples is

Lift = Surface Area  x  CL  x  (1/2  x  Air Density  x  Velocity2)

CL is the Coefficient of Lift, and is determined by both the effectiveness of the cross-section of the surface (something you don't specifically control outside of blade selection) and the angle it makes with the air it is passing through (the 'deploy angle' in KSP).

What is important to get from this formula is that because lift is calculated by multiplying a number of factors together, and lift will generally be equivalent to the weight of the vessel (constant except for gradual reduction due to fuel burn), if ONE of the components is reduced for whatever reason, one or more of the OTHER components must increase to compensate.

One example you've already discovered is that as you ascend and the air becomes less dense, one or more of the other components ( Surface Area, CL, or Velocity) must increase to maintain the amount of lift needed to support your vessel. Typically you won't change the surface area of the blades, so CL (essentially 'deploy angle') must increase and/or Velocity (rotational speed) must increase.

But of course there is a caveat... if the angle the wing/blade makes with the oncoming air is too high, the CL suddenly decreases and ceases almost entirely over a short span, which in turn decreases the amount of lifting force it can produce, which is commonly known as a stall. You can see this happen when you hold your hand out a car window at highway speeds - hold your hand flat (no angle of attack) and your hand is not suspended, but tilt it upward and your hand wants to rise! Keep tilting upward you reach a point where your hand is pushed backward, not upward as the turbulent flow and impacting air give relatively little lift and mostly drag.

Finally a note on air density and stalls - just like water is more dense than air, so the design of 'wings' designed to operate in those two very different densities must differ in their properties because of how density affects the stalling angle of attack; think airplane propeller vs boat prop... less dense air favors longer, thinner airfoils at lower relative angles while more dense water favors stubbier, wider blades at a higher angle. Another example is that because air density decreases with altitude, and you can only increase the angle of attack so much to increase lift, it is velocity (rotational speed) that must make up for the decreasing density, not angle of attack. (Also keep in mind that because lift increases by the SQUARE of velocity, it makes more sense to increase speed rather than angle of attack for high altitudes...)

What you choose in KSP is simply a balance of these factors...  Good luck!

Edited by Wobbly Av8r
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Very helpful answers, thanks to both of you. It's going to take me a while to integrate this info. Props are way more complicated than I thought. 

17 hours ago, OHara said:

if you want to spend time on this kind of thing; you would also decrease the climb speed.

Good to know, I was trying to reach one of the high peaks behind KSC by launching up as fast as possible and hoping the momentum would carry me up, and kept losing all my V and stalling just a few meters short. 

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50 minutes ago, quazarz said:

Very helpful answers, thanks to both of you.

I'm glad I could help, but must give credit to those who passed the knowledge to me long ago!

54 minutes ago, quazarz said:

I was trying to reach one of the high peaks behind KSC by launching up as fast as possible and hoping the momentum would carry me up, and kept losing all my V and stalling just a few meters short. 

This is one of those non-intuitive lessons that all aviators must learn - don't get on the backside of the power curve! It is humorously described thus: If you push on the flight controls, the houses get bigger, if you pull back on the controls, the houses get smaller. If you KEEP pulling back on the controls the houses get bigger even quicker!

You shouldn't feel bad about having to take time to digest this information - there are still people flying actual jets around that end up stalling them because the concept, while not difficult to understand at a fundamental level, is rather more difficult to put into practice. But rest assured it is a truth of flying any vessel which has a thrust to weight ratio of less than "1".

Something of interest that might be of benefit to your purpose is the idea of "translational lift", which is how a helicopter is able to fly at altitudes it cannot hover at; in brief, rather than each blade acting as a wing providing a lifting force through rotation, the entire plane of the rotating blade acts as a circular wing as long as the vessel has enough forward velocity to take advantage of it...

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14 minutes ago, Wobbly Av8r said:

Something of interest that might be of benefit to your purpose is the idea of "translational lift", which is how a helicopter is able to fly at altitudes it cannot hover at; in brief, rather than each blade acting as a wing providing a lifting force through rotation, the entire plane of the rotating blade acts as a circular wing as long as the vessel has enough forward velocity to take advantage of it...

That's interesting. Although I'm using shrouded rotors so it doesn't seem like this will work for this particular craft. 

Also I wonder ( I'm on vacation and just thinking about KSP, otherwise I'd just try it) if there's any reason I shouldn't be using 8 blades instead of the 4 I'm using now. Would that give me double the lift? IRL I imagine it would add turbulence, but is KSP capable of simulating that?

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6 hours ago, quazarz said:

any reason I shouldn't be using 8 blades instead of the 4 I'm using now.

Anecdotal evidence (experimental with KSP) would indicate that yes, more blades generates both more thrust (requiring more power) and more lift. If you simply right-click on a single blade you get the same readouts at the same deploy angle / angle of attack and RPM. but of course, it's only measuring that one blade. Multiply it by the number of blades and you get the overall result, which is single blade x number of blades.

I'm guessing turbulence is not an emulated factor for the rotating installations based on my observations. When I did my test above, regardless of whether I checked on a 2-, 4-, or 8-bladed installation, they reflected the same lift per blade at identical RPM's.

Now the question of whether - or to what degree - translational lift is mimicked for either ducted or unducted installations is a head scratcher...

Edited by Wobbly Av8r
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