Wednesday, November 07, 2007

The most common misconception.

I've had at least 50 people tell me the following:
(Including more than one scientist with a hard science PHD)
Why not put your rocket engine on top so the vehicle will be naturally stable.

This is wrong. It jives with our natural experience of the world, but it is wrong.

A rocket has no natural preference for thrusting UP. The rocket will thrust in whatever direction you point it. This is unusual in out natural experience. It you hang something on a rope the rope has the natural tendency to dangle straight down and only apply force in the up direction. If you attach something to a balloon the balloon only pulls straight up.

So given that the rocket will thrust in whatever direction its pointed and has no natural tendency to point up the rocket can't add any stability.

So if the motor can't add stability is there anything you can do for gravity to add stability? If the gravity field was uniform it would operate on the center of mass appling no torque to the vehicle and thus no stability. On the surface of the earth this is basically the case. The gravity field varies with the square of the radius. In orbit this slight difference can be used to stabilize a spacecraft, but on the surface the effect is so slight as to be undetectable. (On a 2meter high object gravity is 0.999999969 as strong on the top as it is on the bottom)

Our intuition is not completely wrong with respect to where the rocket motor goes, if it's center of thrust is not pointing through the center of mass then the rocket engine will apply a torque and the vehicle will spin. The current unreasonable rocket design has four engines that must be balanced to keep the vehicle from spinning, so in this sense a single rocket motor pointing toward the center of mass would keep the rocket pointed in a constant direction, but that direction would not be preferentially up without some kind of external control.

16 comments:

David said...

Rather than argue, I'll simply suggest this:

Draw a free-body diagram of a hovering rocket with a single motor and the CG below the nozzle exit plane. Do not assume that the rocket is a sphere - draw something like Armadillo's Quad or one of Goddard's early vehicles. Draw one with the angle relative to the inertial frame equal to zero. Draw another with the angle equal to some arbitrary value.

The key question is: Where do you apply the thrust force vector in the free-body diagram?

Paul Breed said...

Draw the diagram without the gravity.

Then draw it with gravity.

All the gravity does is displace the entire frame. It applies no torque to the system restorative or otherwise. You are assuming that the upward facing rocket thrust does not rotate with the rigid rocket.

Draw the hovering rocket slightly off kilter then draw the free body diagram what force is going to restore the rocket to pointing vertical? It will stay off kilter until it experience litho braking ;
)

Paul Breed said...

To be more complete
If the rocket is acting through the
vehicle center of mass then the rocket can not induce any torque.

When you tip the free body diagram you describe, the rocket is no longer thrusting up, it is thrusting at an angle as my origional post pointed out it is very counter to our natuarl experience if forces attached to things in the gravity field. It is also quite correct.

David said...

I drew the freebody diagram as I suggested to you this morning. When I first calculated the sum of the moments, I did so about the CG - the sum was zero and I was disappointed.

However, if you calculate the sum of the moments about another point, say the center of the nozzle exit, they are definitely non-zero.

Another way to think of it is this.

When the vehicle is slightly canted, gravity and thrust are NOT aligned. There is a component of gravity which is perpendicular to thrust (or vice versa). Because the two force vectors are not aligned, a moment (or torque) must result.

Here is my diagram:

http://davidcgregory.dyndns.org/freeBody.jpg

Paul Breed said...

I Think you made an error. If you pick a different reference point for your force body diagram (FBD) then the gravity should be applied at that point.

The system of forces should be linear, calculate the result one force at a time then sum,
or sum the forces and calculate.

So if you turn the rocket off
and calculate the forces due to gravity using your offset origin and gravity applied at the CG you get a torque. We all know that gravity does not apply a torque on a body in free fall.

Given your reference point varying the rocket thrust for 0 to 1000%
does not change your calculated torque.

If you sum about a point other than the CG I don't think that is valid.
(In 6DOF simulations you spend a lot of time calculating the instanious CG and Inertia Tensor to do the calculations)

I'm not sure what calculating off the CG point really does, other than to say that the rocket is following a curved path in earth fixed reference frame as gravity
starts to accelerate it down and the off axis thrust fixed point on the ground then you will see the rocket is following a curved path
toward the ground and in some reference frame that curve could look like a torque.

Anonymous said...

I believe I understand Paul's explanation of why things work the way they do; but if that's true, why did Goddard build tractor rockets before he had gyroscopes to actively stabilize the rocket with aerodynamic vanes?

Presumably the tractor rockets were somewhat successful and stable.

Some simple examination of a bottle rocket (specifically a 'Whistling Moon Traveler' if it matters) indicates that the CG is ahead of the nozzle, in spite of the long stabilizing tailstick. Presumably this indicates that the stabilization of said bottle rocket is primarily aerodynamic, rather than gravitational. So does this indicate that other tractor rocket examples (Goddard's, Apollo/Mercury Launch Abort Systems, old blackpowder military rockets) were aerodymaically stabilized rather than gravitationally stabilized? (Of course, aerodynamic stabilization isn't much use when you have no airspeed, as in a hover).

-- Carl.

Paul Breed said...

Goddard built his original tractor rocket with that stability in mind, but he found out it did not work.

See
http://www.phy6.org/stargaze/Sgoddard.htm

search the page for Stability.

Most rockets in the atmosphere are not designed to hover so they acheive stability by keeping the center of perssure behing the center of gravity.

noel.wade said...
This comment has been removed by the author.
noel.wade said...

I think that's the key point, Paul:

Most people don't realize that you're describing the system in hover (or, alternatively, in the absence of an atmosphere).

As someone who's done aircraft design (admittedly as a hobbyist), I think the physics of "flying something" (which people perceive your rocket doing) includes aerodynamic forces in most people's brains. It doesn't occur to them to take that (and such items as center-of-lift or center-of-pressure) out of the equation.

If you take aerodynamics out of the equation and you lock the thrust vector to the rigid frame of your vehicle, then having your CG/Center-of-Mass below the rocket doesn't inherently add stability.

Imagine a heavy ball attached to a single pole, which then attaches to your rocket. Draw this on a piece of paper (yes, working only in 2 dimensions; that will suffice for this thought-experiment).

Try sticking the pole on to the rocket at different angles. You'll see that it doesn't matter if the ball is above or below the rocket; whenever it is offset to the "side" of your thrust line, you are going to apply a torque and the rocket is going to begin swinging around the ball (don't think about the whole contraption's motion around the earth - just think about the vehicle itself).

Imagine this happening; and insert your own Wile-E-Coyote comic interlude.

The only time the rocket keeps thrusting in the same direction is if the ball is directly above or below the rocket, and perfectly aligned with the thrust vector.

--Noel
(Long time lurking XPrize, Armadillo, & UR enthusiast, pilot, and sailplane designer)

Pierce said...

David: The thrust vector acts, assuming the rocket is balanced and rigid, through the CG, same as gravity. Since the vehicle, while in free flight, rotates around the CG (and no other point), there's just no torque to be had. Your own FBD shows that, if you correct it such that the thrust vector is aligned correctly.

Carl: The tractor rockets didn't work very well. Goddard made the same physics error that David is making, but he got better.

As for the bottle rocket, it is aerodynamically stabilized. The guide stick moves the center of pressure behind the center of gravity, and thereby provides a restoring torque if it gets off course.

Paul Breed said...

Noel,
If you are a long time sailplane developer you would like my previous lunatic project...

http://www.rasdoc.com/splinter/solar2004.htm

(Airfoils designed for me by Dr Drela)

ザイツェヴ said...

This topic reminds me about many people who think that ahedral wing prevents airplane from rolling.

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Anonymous said...

I get most of what youre saying but in the balloon analogy, the balloon is pulling itself up from the top as if a motor was placed at the top of a vehicle. So I don't get that argument.

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