Rocket Idea: Bell-Shaped Pendulum

[sanman]

One idea that just came to me relates to the "pendulum fallacy", whereby people mistakenly think that a rocket is hanging by the nose from an imaginary string, instead of actually resting on top of its tail/thruster.

So then, what if you could position a lot more of the rocket/lander's mass below the thruster?
Then you really would have a little more basis for the pendulum paradigm.
And a pendulum is a little more easy to balance on a vertical centerline than a pencil standing on its end is.

So what if your rocket/lander looked more like a bell shape, where the thruster was located on the inside of the bell near the top, and the fuel tanks with their propellant mass were located on the outside of the bell near the bottom?
Wouldn't that type of mass distribution make it easier to do your balancing act, since your vehicle's mass distribution would be helping you rather than working against you?

Comments? Thoughts?

 

[Cyrus]

I don't understand the point your trying to make here. Rockets work just fine the way they are.

 

[D H]

One idea that just came to me relates to the "pendulum fallacy", whereby people mistakenly think that a rocket is hanging by the nose from an imaginary string, instead of actually resting on top of its tail/thruster.

So then, what if you could position a lot more of the rocket/lander's mass below the thruster?

It appears you don't understand the pendulum fallacy. Do what you said and your rocket will go tumbling out of control. That design is essentially what Robert Goddard's first rocket looked like. It rose 41 feet, tumbled, and crashed. The rocket tumbled precisely because the bulk of the mass of the rocket was beneath the thruster. For a rocket to be stable the center of gravity needs to be above the center of pressure.

 

[sanman]

Hi,

I was mainly thinking about a lander type of vehicle, in the wake of the recent X-Prize lander competition. In that case, the vehicle is mainly hovering, or else descending or ascending in a gradual manner. In that case, wouldn't it be better to have more mass located below the thruster? Surely Goddard's first rocket wasn't a lander, but just a projectile.

 

[D H]

Adding fins obviously isn't going to help stabilize a vehicle that is to land on the Moon. Adding weight to the nose won't help either. If there is no atmosphere there is no center of pressure. Adding weight below the thrusters won't help either. The only way to counter a thruster misalignment with something that is to land on the Moon is with other thrusters.

 

[skeptic2]

Adding weight below the thrusters won't help either.

Why do you say that?

It would seem that having weight below the thrusters, i.e. having the center of gravity below the main thruster, would tend to keep the lander upright without using a gyro or additional thrusters.

 

[D H]

Why do you say that?

It would seem that having weight below the thrusters, i.e. having the center of gravity below the main thruster, would tend to keep the lander upright without using a gyro or additional thrusters.

You are using a false analogy.

The only reason that adding weight to the nose of a rocket launched from the surface of the Earth adds stability is because of the Earth's atmosphere. Atmospheric drags (1) couples the rotational and translational equations of motion and (2) provides a restoring torque if the center of mass is above the center of pressure (aka center of drag).

Sans an atmosphere the rotational and translational equations of motion become completely uncoupled assuming (1) constant mass and (2) the equations of motion are about the vehicle's center of mass. A thrusting rocket obviously does not have constant mass. The coupling due to changing mass properties is typically extremely small. It does become apparent for a vehicle that loses 90+ percent of its mass (i.e., launch), but even then the effect is quite small. For a lander, the rotational and translational equations of motion can be treated as being uncoupled with zero loss of accuracy. Thruster errors and mass uncertainties are many orders of magnitude larger than the errors that result from ignoring this coupling.

So, rotational and translational equations of motion are uncoupled? What does this mean? Simple: It means that mass distribution cannot provide a restoring torque against a thrust misalignment.

 

[sanman]

Well, consider a situation with additional balancing thrusters (attitude control thrusters?) beyond the main thruster providing lift.
Placing the balance-thrusters farther away from the main lifting thruster would be beneficial because the restoring torque from their thrust would be improved.

So, with all other things being equal, if you place your balance-thrusters farther away from the main thrust point which is lifting the rocket, then they will be able to exert more torque on the vehicle mass to correct its attitude. The

I'm wondering if even electric thrusters could be used for balancing purposes, since they would only be responsible for balancing the vehicle, and not for directly lifting it. I'd imagine that they'd be more reliable than chemical thrusters, though I'm not sure if they're superior to just gimbaling the main thruster for attitude control and balance.
Does anybody know what mechanism is used for gimbaling?

 

[sanman]

Adding fins obviously isn't going to help stabilize a vehicle that is to land on the Moon. Adding weight to the nose won't help either. If there is no atmosphere there is no center of pressure. Adding weight below the thrusters won't help either. The only way to counter a thruster misalignment with something that is to land on the Moon is with other thrusters.

Well, if you look at the X-Prize lunar lander competition, the main contenders seem to have a lone main thruster mounted on gimbals, which can be swiveled as needed.

I wonder how small thrusters for balancing would compare to the weight of a gimbal system?

 

[DaveC426913]

Well, consider a situation with additional balancing thrusters (attitude control thrusters?) beyond the main thruster providing lift.
Placing the balance-thrusters farther away from the main lifting thruster would be beneficial because the restoring torque from their thrust would be improved.

In principle you have a point, but in practice:
1] more motors means more mass, more complexity and more things to go wrong. You want it as simple as possible.
2] you're trying to solve a problem that doesn't really exist. The pitch/yaw is not so appreciable that the current technique needs improvement.

 

[D H]

So, with all other things being equal, if you place your balance-thrusters farther away from the main thrust point which is lifting the rocket, then they will be able to exert more torque on the vehicle mass to correct its attitude.

Spacecraft designers try to place their attitude thrusters far from the center of mass.

I'm wondering if even electric thrusters could be used for balancing purposes, since they would only be responsible for balancing the vehicle, and not for directly lifting it.

No. Not yet, anyhow. The electric thrusters developed to date generate tiny, tiny amounts of thrust. If your goal is to provide exceptionally fine control of vehicle attitude, goal accomplished. You would need to fire electronic thrusters for quite some time just to effect a tiny, tiny change in attitude in a vehicle the size of the lander for the X-Prize competition -- assuming of course the only things firing are your electric thrusters.

If on the other hand, your goal is to provide controllability, electric thrusters are (currently) not the way to go. They simply do not have enough oomph to compensate for thruster misalignments and mass properties uncertainties.

I'd imagine that they'd be more reliable than chemical thrusters

Why in the world would you imagine this? Scientists and engineers are still working on solving the feasibility problem when it comes to electric thrusters. To wit, can we make electronic thrusters that provide reasonable amounts of thrust? Until they address this problem, the reliability problem is completely moot. A couple of things we do know from history: (1) Scaling tends to create reliability issues. (2) Prototypes typically do not address reliability problems. They are concerned with more basic problems (can we do it).

Another way to look at it: We've been building chemical thrusters for well over half a century. We know a lot about reliability of chemical thrusters. We don't know jack about reliability of electronic thrusters.

though I'm not sure if they're superior to just gimbaling the main thruster for attitude control and balance.
Does anybody know what mechanism is used for gimbaling?

Gimbaled engines have all kinds of reliability issues, which is why spacecraft designers use gimbaled engines only when there is no alternative. Gimbaling is done with messy, failure-prone hydraulics systems.

 

[skeptic2]

You are using a false analogy.

The only reason that adding weight to the nose of a rocket launched from the surface of the Earth adds stability is because of the Earth's atmosphere. Atmospheric drags (1) couples the rotational and translational equations of motion and (2) provides a restoring torque if the center of mass is above the center of pressure (aka center of drag).

Sans an atmosphere the rotational and translational equations of motion become completely uncoupled assuming (1) constant mass and (2) the equations of motion are about the vehicle's center of mass. A thrusting rocket obviously does not have constant mass. The coupling due to changing mass properties is typically extremely small. It does become apparent for a vehicle that loses 90+ percent of its mass (i.e., launch), but even then the effect is quite small. For a lander, the rotational and translational equations of motion can be treated as being uncoupled with zero loss of accuracy. Thruster errors and mass uncertainties are many orders of magnitude larger than the errors that result from ignoring this coupling.

So, rotational and translational equations of motion are uncoupled? What does this mean? Simple: It means that mass distribution cannot provide a restoring torque against a thrust misalignment.

I appreciate your reply and your generous explanation. However, as I'm sure you know, there are three types of rotational motion that apply to an aircraft or spacecraft , pitch, roll, and yaw. Do you mean to say all three are uncoupled from the translational motion of the rocket while it is thrusting?

 

[D H]

I appreciate your reply and your generous explanation. However, as I'm sure you know, there are three types of rotational motion that apply to an aircraft or spacecraft , pitch, roll, and yaw. Do you mean to say all three are uncoupled from the translational motion of the rocket while it is thrusting?

Roll, pitch, and yaw are not three different types of rotational motion. Those are three arbitrary terms applied to an arbitrarily chosen set of orthogonal axes. They typically don't even represent the vehicle's eigenaxes. (I have yet to work with a spacecraft with a diagonal inertia tensor in structural frame, let alone body frame, coordinates.)

Ignoring changes in mass properties (a very good approximation exception during launch), the rotational equations of motion expressed in body frame coordinates are

<br /> \boldsymbol I \dot{\mathbf \omega} +<br /> \boldsymbol I \mathbf \omega \times \mathbf \omega =<br /> \mathbf\tau_{\text{ext}}<br />

where

• I is the vehicle's inertia tensor expressed in body frame coordinates about the vehicle's center of mass. This ideally is a diagonal matrix. In reality, it never is diagonal. There is only so much room inside a vehicle. There's always something that has to be jammed into some weird spot that makes the inertial tensor non-diagonal.
• ω is the vehicle's angular velocity vector. This had better be very low during landing. Ideally, it will be one revolution per month for a lunar landing.
• Iω×ω is the inertial torque. The body frame is not an inertial frame. Think of this as the rotational analog of coriolis force. For low angular velocities, this term is practically null.
• τ_ext is the external torque. This is where the coupling between rotational and translational motion comes into play when flying through an atmosphere. The aero drag torque depends on velocity with respect to the atmosphere. The Moon has no atmosphere, there is no aero drag torque. There will be a smallish gravity gradient torque. The vast majority of the external torque will come from the thrusters. A thruster whose thrust is supposed to, but never does, pass through the vehicle centerline will generate a torque. If instead of using one central thruster you are using three or four supposedly balanced thrusters, well, they aren't balanced in reality.

Here's the killer regarding torque from misaligned / not quite balanced thrusters: It is constant in the body frame. It rotates with the vehicle. Without correction, it just spins the vehicle up faster and faster.