Monday, November 05, 2007

The Agony of the valves.

After spending a few days at XPC it's very clear that our system is too complex.
KISS Keep It Simple Stupid.

The temptation is very great to start over from scratch and redesign everything. If I were to start again I would design something that looks a lot like pixel or the Armadillo Quad, a Single engine. The counter to this is that the only thing we really need to finish our vehicle is fast robust reliable valves. Its always tempting to trade the devil you know for the invisible devil lying in the green grass on the other side of the fence. Everyone I've talked to in Alt space has had valve problems of one kind or another.

My core problem is that I need very fast (50 to 100msec) control of the engine thrust to maintain reliable attitude control. Our vehicle is relatively small so that it's overall rotational inertia is low, and the motors are on the very outside of the vehicle this combines to require fast/precise control of the motor thrust.

How fast?
We can do some freshman physics and figure that out.
Lets assume that the vehicle is 2m diameter sphere.
(This is a slightly pessimistic view of our inertia the vehicle will be more stable than this)

I=2 mr^2/5 =2m/5

We are hovering with 4 motors. The total required lift is mg
So the force for each motor is mg/4

The motors are thrusting on a 1 meter lever arm from the Cg.

Now assume we can very the thrust in 1% steps around nominal.

Assume we increase the thrust in one motor by 1% and decrease the opposite motor by 1%

torque=1 * 2%mg/4

angular acceleration alpha=torque /I =(1*0.02mg/4)/(2m/5)

alpha = 0.0125g (notice m drops out)

or assuming g=9.8m/sec

alpha = .1225 radians/sec ^2

If we want 1 degree control of the vehicle 1 degree = 0.01745 radians.

The rotation is just like linear acceleration angle = (alpha*t^2)/2

So for 1% motor change a 1 degree error occurs in t=.53 seconds.

We would like our control to be about 5x to 10x the speed hence we need a 50msec valve.

How do we get such fast control:

Monster actuators and normal ball valves.
95% Off the shelf.
Lots of hysteresis (3 to 5%), Seals wear out quickly.
Hysteresis really complicates the control system.

Voice coil driven piloted spool valves.
Such things exist for Hydraulic systems.
Control response as fast as 15msec 0 to 100%
Hysteresis 0.1% Basically a perfect valve.

No off the shelf valves will work for LOX
Serious engineering effort to build such a valve in a Lox compatible way.

More complicated Odd combinations.

One can start doing things that add significant complexity:
Adding modulated water injection.
Modulating just the fuel supply while leaving the LOX on a slow actuator.
Using a pile of fast solenoid valves
One fast Solenoid valve as trim with Slow ball valve following.

Potentially the lowest cost option.

Violates KISS
Requires a lot of development testing.

I'm sure I'll post more on this in the coming days and weeks.


g said...

Sounds like a tough problem. I guess one could try to maximize the diameter of the vehicle to get a big inertia.
One could put the tanks in a horizontal arrangement to make the whole vehicle more of a flat cross.
The inertia of a rod is 1/3 * m r^2. (There are four rods each with 1/4 m.) If one can double the diameter r to 2 m at the same time then the inertia grows (4m/3)/(2m/5)=10/3 fold but the lever arm grows to double too so the time factor only less than doubles, from 50 ms to 80 ms. (And the ball estimate was conservative, in reality the benefit is even less.)

I guess one could also move the engines closer to the center. How hard would that be? I understand your current engines are directly bolted to the tank (just a regulator and a valve).
The vehicle could be W shaped. :) Landing gear could be interesting. Or just a wide H shaped. You lose structural efficiency with all those, your current configuration being extremely nifty in that regard.

I don't know if a single engine in the middle would be that easy either, you'd need some pretty fast and strong actuators for gimballing that too, and flex hoses.

Paul Breed said...

I think I'll look at mounting the motors Uner the tanks toward the inside still structurally efficent and allows us to simplify the landing gear to Rubber donuts at the outside of the tanks.

Anonymous said...

This might be somewhat of an oversimplification, but what if you mounted the motor(s) in the center of your vehicle? The weight of those propellant tanks would then be below the center of thrust, making the vehicle naturally stable when it hovers. Wouldn't that be easier?

Paul Breed said...

The position of the motors has a control authority effect, but does not contribute to stability.This is the most common misconception I hear about rockets.

A thought experiment
Disregard aerodynamic forces.
The vehicle is Rigid.

Now assume that the vehicle is floating in space and can be pointed in any random direction thrusting at 1G

It can point in any orientation no orientation is preferred.

Now to that picture add an external 1G gravity field. The external 1G field will operate on the center of mass and will induce no torque.

If it can apply no torque to the vehicle how can it add stability?

The key is the rocket motor pushes in whatever direction its pointing.
It has no preference for pushing up. Most of our Natural experience is with things like ropes tied to one point or balloons or something solidly attached to the ground where the natural forces line up with gravity and the force applied has a direction varying component.

Jon Goff said...

Out of curiousity, how fast of reaction time were you getting out of your butterfly valves? Is the reason you're looking at changing valve concepts because the butterfly valve setup wasn't working or wasn't working fast enough, or is this just a concern about complexity?

Just curious because we had actually looked at a similar approach (ball for shutoff, butterfly/throttle plate for throttling) about a year ago, but were unable to give it a try at the time.