Stock VTOL Planes still have uncontrollable torque

[SchweinAero]

31 minutes ago, Rocket In My Pocket said:

The important thing for this conversation is that it does actually produce a noticeable improvement in stability which players can utilize.

I'm still inclined to think the effect is psychological, but I will now make sure to test it for myself. It might have something to do with the aerodynamic forces on vertical and angled nacelles with lateral velocity. 

Edit: the results are in and it seems @Dafni was right. Having engines far from the CoM and tilted toward the CoM are two ways to give their gimbals a longer lever arm - better control authority. If you lock gimbals, all-vertical and tilted setups work identically except for thrust loss. 

Edited August 13, 2017 by SchweinAero

[Rocket In My Pocket]

34 minutes ago, SchweinAero said:

I'm still inclined to think the effect is psychological, but I will now make sure to test it for myself. It might have something to do with the aerodynamic forces on vertical and angled nacelles with lateral velocity. 

Edit: the results are in and it seems @Dafni was right. Having engines far from the CoM and tilted toward the CoM are two ways to give their gimbals a longer lever arm - better control authority. If you lock gimbals, all-vertical and tilted setups work identically except for thrust loss. 

Hmm, so it might still have some effect for gimbal engines?

Very interesting. Thanks for doing the testing, I was just about to myself.

All this talk about it was making me curious. I actually haven't done it since I was a new player because I just got better at balancing the planes in the first place, lol.

[Xyphos]

15 minutes ago, Rocket In My Pocket said:

I actually haven't done it since I was a new player

same here, and usually I don't build such large vessels as this one, but I wanted to challenge myself anyway.

[Dafni]

1 hour ago, SchweinAero said:

Edit: the results are in and it seems @Dafni was right. Having engines far from the CoM and tilted toward the CoM are two ways to give their gimbals a longer lever arm - better control authority. If you lock gimbals, all-vertical and tilted setups work identically except for thrust loss. 

Thank you for this. I was pretty convinced I understood how the game does this, but who am I to argue with Val? Started to doubt my own logic there.

[Rocket In My Pocket]

1 hour ago, Dafni said:

Thank you for this. I was pretty convinced I understood how the game does this, but who am I to argue with Val? Started to doubt my own logic there.

Same, seeing a mod support the theory definitely had me convinced.

[EnderKid2]

5 hours ago, Dafni said:

you can not individually throttle engines

You can

 

Edited August 13, 2017 by EnderKid2

[KerikBalm]

3 hours ago, Rocket In My Pocket said:

Hmm, so it might still have some effect for gimbal engines?

Definitely, if the center of thrust is right at the COM, then gimbal will not be any use for pitch authority.

Its the same reason that "shuttles" don't flip out uncontrollably despite the engine thrust not being aligned with the flight vector: the thrust vector goes through the center of mass. If your center of thrust is right on the center of mass, it will go through the center of mass no matter which way you vector the thrust.

You need the engines to be placed in a way that vectoring them can cause thr thrust vector to move in front of or behind, or right through the CoM

[EpicSpaceTroll139]

11 hours ago, Rocket In My Pocket said:

I never said anything about downward force, I'm just quoting what a moderator said about it since it supports my conclusion that this is an actual tangible effect others see in the game and it's not just me being crazy. Lol.

My bad. Didn't mean to put words in your mouth.  I was indeed referencing the moderator. 

And don't worry, I don't think your crazy xD. I just think the effect you see is the result of sort of side-effect of the canting, the changing engine gimbals' moment arms like @Dafni

Edit: my bad, the auto-sort-by-votes thing threw me off on what you all had been saying. Again...

Edited August 14, 2017 by EpicSpaceTroll139

[Snark]

Just wanted to weigh in here 'coz my Nerd Sense was tingling-- folks' talkin' smack about physics.  Ahem. 

Anyway, some misconceptions appear to be floating around here, so a few words from an old physics nerd.  Warning, massive wall of text incoming.

 

On 8/13/2017 at 4:47 AM, Rocket In My Pocket said:

Let's say you have 4 lift engines placed around the COM, if they are straight up and down your plane is being lifted on a very narrow column of thrust making it tippy and unstable.

Angling them out widens the base of this "pillar" and provides more stability.

No.  Physics doesn't work this way.  An object that generates thrust at a location is just a force vector.  If you have multiple of them mounted to a rigid body at fixed angles, then the sum of their effects is precisely that:  the mathematical vector sum of their effects.

If you mount two 100 kN engines pointing straight down, spaced equidistantly apart from the CoM, then the net effect of their thrust is 200 kN pointing straight down, behaving as though it's acting on the CoM.   If you take those two engines and then symmetrically angle them outwards by N degrees, you get the exact same thing-- the only difference being that you lower the effective thrust due to cosine losses.

And that's regardless of the orientation of the ship.  Angling the engines outwards does not provide any inherent stability based on the above explanation.

There is no "pillar".

Now, what does matter is whether the CoM is above or below the plane in which the thrusters are located-- if the CoM is below it, you'll have a stable arrangement; if the CoM is above it, you'll have an unstable one.  I suspect that this is the real reason for the VTOL instability:  the lift engines are mounted underneath, with the CoM located above the CoT of the engines, which means it's like trying to balance a pyramid on its point-- it wants to be upside-down.

On 8/13/2017 at 4:53 AM, Dafni said:

Unfortunately this is not true in KSP. You dont get a "pillar" of thrust. You are always balancing on the same "needle" of thrust, as KSP simulates a combined vector of thrust just as such, a vector, no matter how far away from each other you tilt the engines.

^ This.  Exactly this.  And by the way, it's not true in KSP because it's not true in reality.  KSP simulates a combined vector of thrust because that is in fact how reality works.

On 8/13/2017 at 4:55 AM, Rocket In My Pocket said:

*Cough cough.*

If angling the engines outwards actually works in KSP, great-- but if it does, it's not because of the supposed physics argument about "widening the base of the pillar".  My guess would be that it's likely something to do with the SAS control of the engine gimbals.  I'm guessing that if you turn off SAS, or lock the engine gimbals, you'll see the benefit from outward-angled engines go away.

In other words:  all VTOL craft with CoT below CoM are inherently unstable, according to physics.  To fly stably, therefore, they need help from software, since physics is against them.  SAS manages this by gimbaling the engines.

However, gimbaling the engine only helps you if the engine has a decent lever arm to work with.  For example, picture a gimbaling engine like a Panther located in the traditional spot, facing rearwards on the back end of a plane.  If that engine is located far behind plane's CoM, then it has a lot of lever arm to work with, so gimbaling provides a lot of torque and can really stablilize the plane with SAS.  But if the engine is located amidships, right next to the CoM... then gimbaling the engine helps not at all for stability, because it has no lever arm.

If you have VTOL engines pointing down, chances are good that their CoT is below the plane's CoM.  However, unless they're sticking way down as if your plane's on stilts, chances are that that they're only slightly below the CoM.  Which means that they've got a really short lever arm to work with, which means they can't do much to try to fix the plane's inherent instability.

On the other hand, if you angle the engines outwards... now it's a different ball game.  Because remember, the amount of torque an engine gimbal can get depends on the lever arm, which is how far "behind" the CoM the engine's CoT is... in the engine's frame of reference.   And tilting the engines so that their exhaust point outwards is (in each engine's frame of reference) rotating the CoM "forwards", putting the engine farther "behind" the CoM and giving it a bigger lever arm to work with.

Think of it this way.  Imagine you've got a VTOL aircraft with four engines.  The engines are mounted such that each engine's CoT is located, say, 5 meters left or right of the centerline (and CoM) of the aircraft.  Let's suppose that the engines are mounted such that the CoT is slightly below (i.e. ventral to) the aircraft's CoM-- let's say, 50 centimeters.

Consider the following scenarios:

• Engines are pointed straight down.  In this case, every engine is, in effect, only 50 centimeters "behind" the center of mass.  Their engine gimbal has a 50-centimeter lever arm to work with.
• Engines are pointed straight outwards, i.e. horizontally.  The left engines are pointing straight left; the right engines are pointing straight right.  Yes, that's silly, it will generate no lift and won't help the plane go anywhere.  But note that every engine now has a 5-meter lever arm to work with.  The engines can't move or lift the plane... but they can torque the heck out of it.  They have ten times the lever arm that the vertically-mounted engines do.

So, mounting the engines perfectly vertically gives them optimum power to lift the plane, but makes it really hard for them to stabilize it.  Whereas mounting them horizontally completely removes their ability to lift, but gives them optimum power to stabilize.

"Angled" engines, such as from @Rocket In My Pocket's screenshot, will occupy a space between those two extremes.  You lose some lift due to cosine losses, but you greatly magnify the lever arm of the gimbals, adding much more stabilizing power.

For anyone who wants the math, check the spoiler section.

Spoiler

Let's assume you have a VTOL aircraft whose lift engines have located distance x left and right of the aircraft's centerline, and vertical distance y below it.  (By "location" I refer to the CoT.)

Let's assume that the engines are rotated to direct their thrust outwards by angle θ, such that θ = 0° corresponds to a perfectly vertical engine, and θ = 90° corresponds to an engine pointing its exhaust horizontally straight outwards (i.e. leftwards for a left engine, rightwards for a right engine).

The torque arm r of the gimbals (and therefore the amount of stabilizing authority they can exert) will be given by:

r = (x * sinθ) + (y * cosθ)

So, suppose we have a case where x = 5 meters, y = 0.5 meters.  How does the lever arm break down?

• θ = 0°:   r = 0.5m
• θ = 5°:   r = 0.93m
• θ = 10°:   r = 1.36m
• θ = 20°:   r = 2.18m
• θ = 30°:   r = 2.93m

As you can see, even a little bit of outward angling makes a big difference here-- even just 5 degrees nearly doubles the amount of control authority available to SAS via gimbaling!  A 20-degree angle more than quadruples the stability.

And actually, it's even more extreme than that.  Because what we really care about is not the lever arm r, but rather the torque produced, τ, which is the product of lever arm with thrust.

Why is that relevant?

Because you need more thrust if your engines are angled outwards, to compensate for cosine losses.  If a person angles their engines outwards... they lose some lift due to cosine losses... which in turn means they need to mount more engine thrust per kilogram of plane in order to maintain lift.  So they add engines to the plane to make up for the lost lift... which directly magnifies the control authority of the gimbal.

This introduces another cosine term into the above equation.  Basically, the stabilizing torque is going to be proportional to (x * sinθ) + (y * cosθ) divided by cosθ.

So, let's take the above set of possible angles, and take this into account.  I'll normalize it so that the straight-vertical case has a "stabilizability" (gimbal torque) of 1.

• θ = 0°:   1.00
• θ = 5°:   1.87
• θ = 10°:   2.76
• θ = 20°:   4.64
• θ = 30°:   6.77

Q.E.D. 

So, there you have it.  Tilting your engines makes you more stable because it gives the SAS a bigger lever arm to work with when gimbaling the engines.  It has nothing to do with "widening a pillar".

On 8/13/2017 at 5:00 AM, Dafni said:

I stand corrected.

No, you don't.  You were exactly right.  Your physics is spot on.  It's SAS and engine gimbal that make the difference, here.

 

On 8/13/2017 at 5:05 AM, Rocket In My Pocket said:

I might still be wrong about the wide pillar of thrust thing

Yes, you are.  Completely and utterly dead wrong.  But don't worry, we still like you anyway.    It's an easy mistake to make; look at all the people who think that reaction wheel placement matters in terms of how rapidly they can rotate the ship.  "Intuition" is often wrong.  It's physics that answer questions.

 

On 8/13/2017 at 6:08 AM, EpicSpaceTroll139 said:

Ermm.... but "downward force" doesn't mean anything? Say I have a vtol with 2 engines mounted 3m to the sides canted 10 degrees out. When the VTOL is level, they produce 0 net torque. 

Now let's say the VTOL tilts over to 10 degrees. The engines are still in the exact same positions on the ship, just on happens to be tilted 0 degrees relative to the surface of Kerbin (or whatever planet), and the other 20 degrees. They are still producing the exact same thrust and in the exact same positions on the ship, therefore they also produce 0 net torque. Your overall thrust vector is now tilted 10 degrees. The only way you would get any stabilization would be with special aerodynamics and/or ground effects, which we do not have.

You might want to take a look at this, as it is a fallacy that would have similar stabilization effects: https://en.wikipedia.org/wiki/Pendulum_rocket_fallacy

Try turning off SAS in a vtol with the engines canted out. If such a stabilization effect occurs, it should stay in a hover on its own. But it won't, it will slowly (or quickly) tip over until it crashes into something, in the exact same way as one without canted engines.

Given how close the engines are to the horizontal plane of the uh, plane, I'm guessing what might be experienced as a "stabilizing effect" is the engine gimbals having more power over the aircraft's attitude. (It's hard to explain why this works in words, I'll try to make a picture explaining it in a bit, perhaps when I get back from work)

^ This.  This right here.  This exactly captures it.

 

On 8/13/2017 at 7:29 AM, Rocket In My Pocket said:

I'm just quoting what a moderator said

...Bearing in mind that moderators don't have any more special knowledge of how the game works (or how physics does) than an average user does.  They're an authority on what's permissible in the forums.  The "moderator" aegis does not confer any arcane physics knowledge.

For example, on this topic, I happen to be right.  But I'm not right because I'm a moderator, I'm right because I'm a physics major. 

 

On 8/13/2017 at 7:29 AM, Rocket In My Pocket said:

who's to say why or how it works

Physics says.

 

On 8/13/2017 at 7:29 AM, Rocket In My Pocket said:

it's just a video game with a very arbitrary definition of physics.

Actually, it has a pretty accurate definition of physics.  It's modeling how things actually behave.  Granted, it's an arbitrary model of how airplane parts are engineered (size, mass, ability to gimbal, how fast it gimbals), and an arbitrary control model for SAS.  But the physics are pretty accurate, actually.

 

On 8/13/2017 at 7:44 AM, SchweinAero said:

I'm still inclined to think the effect is psychological

I think it's physical, not psychological-- but the reason lies in the SAS gimbal authority, rather than the sum-of-forces of the engines.

 

On 8/13/2017 at 7:44 AM, SchweinAero said:

Edit: the results are in and it seems @Dafni was right. Having engines far from the CoM and tilted toward the CoM are two ways to give their gimbals a longer lever arm - better control authority. If you lock gimbals, all-vertical and tilted setups work identically except for thrust loss.

...Aaaaand there we have it.  Ta dah! 

 

On 8/13/2017 at 10:24 AM, Rocket In My Pocket said:

Same, seeing a mod support the theory definitely had me convinced.

Again:  just because someone's a moderator is not a reason to take their word for how the game works.  Expertise with KSP, or with physics, is orthogonal to Super Moderator Powers.

 

[Dafni]

Thank you @Snark for the confirmation. I know a good bit of physics and was pretty convinced I understood how the game "simulates" multiple engines etc. Still nice to get confirmation, even if its just for the sake of other visitors following the discussion.

On top of that, sometimes I'm not only starting to doubt my own logic, but also my ability to translate it into the english language. And your confirmation covers that doubt too, thanks again buddy.

Edited August 19, 2017 by Dafni

[Rocket In My Pocket]

20 hours ago, Snark said:

But don't worry, we still like you anyway. 

Phew, now I can sleep at night. 

[stormdot5]

I think there is another factor at work here that is due to the way KSP deals with controls rather than the physics of the situation.

 

On 18/08/2017 at 5:01 PM, Snark said:

 

Now, what does matter is whether the CoM is above or below the plane in which the thrusters are located-- if the CoM is below it, you'll have a stable arrangement; if the CoM is above it, you'll have an unstable one.  I suspect that this is the real reason for the VTOL instability:  the lift engines are mounted underneath, with the CoM located above the CoT of the engines, which means it's like trying to balance a pyramid on its point-- it wants to be upside-down.

 

On 18/08/2017 at 5:01 PM, Snark said:

In other words:  all VTOL craft with CoT below CoM are inherently unstable, according to physics.

 

I think these two items need to be addressed as they are a bit of misinformation in an otherwise well thought out post. It's funny that these appear as you've quoted and agreed with EpicSpaceTroll139 who has linked the specific explanation of why this does not work: Pendulum rocket fallacy

I think it might be simpler to say that you cannot arrange your engines for inherent stability on a VTOL.

 

To explain the issue of how to arrange engines to give them the best control of orientation, including stability when using SAS, I think the best answer is throttle controlled avionics, as linked above by EpicSpaceTroll139

The reason for this is that the normal position of engines when building a VTOL, arranged around the center of mass, puts them in the best location to provide torque to rotate/stabilise the craft. However, they cannot apply torque as the throttles are all linked and each engine counteracts it's opposite. Allowing them to throttle individually shows they can provide lots of torque and therefore be used to stabilise the aircraft.

 

Discounting mods, the stock SAS only provides control though gimballing (ignoring reaction wheels). When a rotation command is input from the player or the SAS, both opposing engines gimbal the same amount, reducing torque around the center of mass equally in both directions, and trading it for translation. See picture A, The blue arrows show no net torque, and the green arrows show the resulting translation.

http://i.imgur.com/0j3sTAf.png

This means that engines on the same level as the center of mass cannot provide any rotational control.

So if we rotate the engines in towards each other and then apply the same rotation command we get image B. The built in angle is offset by the gimble on the left engine, meaning it provides a lot of torque around the center of mass. This is only weakly opposed by the right engine, which puts it's thrust into translation instead. The result is a net torque and ability to control the rotation of the craft.

In picture C the engines are located below the level of the center of mass. This is exaggerated but effectively during a rotation command the left engine is providing thrust almost perpendicular to the line to the center of mass, giving only torque, whereas the right engine is aligned with the center of mass providing only thrust. This would be the same if the engines were above the level of the center of mass.

 

So how should you arrange your engines?

 

If they have to be on the same level as the center of mass, then angling them in gives you some control. However, as Snark pointed out you need more overall thrust to lift the craft. This means that the craft will be wasting fuel in when VTOL mode.

If you can lower them below or above the level of the center of mass then you can provide control authority and only require the minimum thrust to lift the craft therefore being efficient. There will be a translation induced while you are holding the controls, but it should be minimal.

If you are really serious about VTOLs, then it's probably best to try out throttle controlled avionics.

 

 

It's worth noting that KSP could provide the same functionality as TCA without individual throttles. If a player or SAS makes a rotation command, and the net effect of gimballing the engines is very little rotation, then don't gimble the engines on the side the the player requested. The net torque should provide some rather than no control authority.

 

Edited August 23, 2017 by stormdot5
Insert picture

[Snark]

2 hours ago, stormdot5 said:

I think these two items need to be addressed as they are a bit of misinformation in an otherwise well thought out post. It's funny that these appear as you've quoted and agreed with EpicSpaceTroll139 who has linked the specific explanation of why this does not work: Pendulum rocket fallacy

Whoops.  Excellent point, you're perfectly right.  It's worth noting that a VTOL is a somewhat different situation than a rocket, since unlike a rocket, there is a "preferred" frame of reference for a VTOL (i.e. "zero velocity with respect to the air").  But that's beside the point here, because even taking that into account, my side comment on that topic was wrong, precisely because of the pendulum fallacy.  Wasn't thinking clearly, can't believe I said that.  Thanks! 

That said, though, I think the main point of my post (about lack of inherent stability, and the effects of SAS / gimbaling when engines are tipped or not) is still valid-- basically, the exact same thing that you've so excellently illustrated above.  Great diagrams! 

[Palaceviking]

ENOUGH!  Sorry about that,.  Right,  what you have to visualise with vtols is your focus of thrust(someone please make a mod for this!) which is where straight lines through your various thrust vectors would meet(we'll worry about torque balancing in a moment). 

Now, the relationship between your focus of thrust and centre of mass is almost identical to the relationship between your col and com when building ordinary planes,  so closer together =more nimble,  further apart =more stable.

Stability can easily be applied by thrust limiting/mixing engines and placing your focus of thrust directly on or slightly above your col.

This approach will allow you to tilt engines willy nilly and make stuff that looks quite cool.

Btw, if you want your craft to tilt slightly forward as it speeds into take off then focus the thrust very slightly behind your com and directly into your col.