Calculating the weight of a spacecraft

[Texun]

This is a trivial question that's been bugging me for a few days. There's no class grades or bets are riding on the answer.

I recently stumbled across some Apollo 11 audio tapes, and in the recordings I heard numerous remarks about the weight of the spacecraft right down to the pound. The weight changed (dropped) throughout the flight and I started to wonder how NASA could come up with such an precise number.

My initial assumption is that they start with the known weight of the loaded spacecraft and then deduct consumables throughout the flight by determining the amount used, or produced (waste), and converting said mass to pounds simply by multiplying the units. Does anyone know if they used something more scientific, or was it just a matter of keeping track of fuel, water, explosive bolts, side panels blown away, etc and subtracting that from the loaded weight?

They were very specific so I am guessing they must have had dialed in a plan that would be a perfect fit for their orbital and trajectory calcs which of course would be essential for an accurate orbit, landing, return, reentry and so on.

My hunch seems overly simple for NASA but can anyone tell me if I am even close? :hmm:

 

[firewolfsm]

It would be possible to measure to measure mass through measuring acceleration while thrusting, but they were not always doing that...if the craft was rotating and they secretly developed some way to measure gravitational waves accurately enough that could work...

Oh! They could put a spring on the side of the ship and get it shaking and measure vibrations in the hull, yes, that's how they'll do it. The weaker the vibrations, the more massive the ship.

 

[Fayd]

It would be possible to measure to measure mass through measuring acceleration while thrusting, but they were not always doing that...if the craft was rotating and they secretly developed some way to measure gravitational waves accurately enough that could work...

no, not possible. the hill sphere of that apollo orbiter would be something like a few centimeters. it couldnt generate its own gravitational field strong enough to make objects orbit it...

Oh! They could put a spring on the side of the ship and get it shaking and measure vibrations in the hull, yes, that's how they'll do it. The weaker the vibrations, the more massive the ship.

i thought he was asking for accurate ways to measure.

op: the only practical way i can think of is mass in - mass out.

 

[RocksteadyDotNet]

In space it would weigh nothing.

You're talking about mass.

 

[fteoath64]

It would be possible to measure to measure mass through measuring acceleration while thrusting, .

Yep, I think this is it. They get a quick measure for a few second using mass-estimates, then quickly re-calibrate the thrusting force to decelerate. In the many many seconds during descent. it is easy to re-calibrate it to be almost as good as needed for a decent landing. In fact, I think the thrusters has this routine already built-in.

 

[The Boston Dangler]

i think mass could be determined without thrusting if you rotate the body with a flywheel.

 

[Hacp]

massin+mass out=mass accumulated.
energyin+energyout=energy accumulated.
e=mc^2

 

[Texun]

I assumed there must be an easier and more accurate method than counting the number of explosive bolts, solids, fuel used, etc. They must have had some hard core mathleats up front in the trenches - minimal computing power and lots of slide rules and no room for mistakes.

I listened to a short piece again and they had it down to the decimal: 197,312.9 pounds! Of course that changed as the mission progressed, but it presented an interesting physics quiz.

 

[CycloWizard]

massin+mass out=mass accumulated.
energyin+energyout=energy accumulated.
e=mc^2

True, except e=mc^2 doesn't much to do with this...

It's been quite a while, but I think the fundamental equation of rocket science involves the mass of the ship and the mass of fuel:
http://en.wikipedia.org/wiki/Rocket_propulsion

 

[Farmer]

Well okay, my thinking:

I guess for back of the envelope, you can approximate using energy. A significant amount of the mass (like, I don't know, 90&#37 will be fuel, which is unknown. Suppose you know the mass of your payload (that is, everything needed to keep your crew alive and well for the duration of the mission). Suppose we do an Earth-Moon mission. Suppose you want to place some mass on the moon. Suppose you have a model of the Earth-Moon gravity field, and suppose you have a planned path from Earth to Moon. Then the theoretical energy required to do that mission is just difference in potential between the two points (this ideal gravitation field is conservative). Base on the propellant you use, you know enthalpy change from reaction in something like [Energy]/[Mass]. Suppose you can characterize your motor by some efficiency factor (that is, the power in thrust some some fraction n of the chemical energy stored in the fuel). Then, by combining the three, you should have a first order approximation of the required fuel mass. Add fuel mass to the mass you get from your approximation of the payload mass, and you get a first order mass estimate.

I worked at Glenn for summer in mission analysis, so I learned a tiny bit. For a real mission, you need to know a lot of things. Generally, I believe mission planning is done using computer-based optimization codes. That is, you set up some arbitrarily complex gravitational situation (say, the solar system), and you want to go from A to B. You set up some constraints on your path (like, can't fly into Sun or must take less that 100 years), then you choose some optimization condition, like, minimize fuel consumption (i.e., the required momentum change for you to get from point A to point B). Assuming the code can converge, after iterating using some numerical method*, you will get an answer. I've seen this done on a program called COPERNICUS, which has a GUI was written by UT professor, but from what I've seen NASA likes to use a more flexible albeit a little more esoteric program called OTIS.

*You pretty much have to solve numerically, as the general n-body gravitational problem is analytically intractable, but I'm sure accurate numerical methods have been developed. When I say numerical method, it's something similar to Newton's method or ODE methods like Euler or Runge-Kutta that people typically see in college.

 

[DrPizza]

In space it would weigh nothing.

You're talking about mass.

I hate to bump an old thread, but it has weight. If I dropped a rock from 10 feet above the ground, would you say that the rock has no weight while it's falling? The rock is in free-fall. I certainly agree that he's talking about mass; and the scientists back in the day treated pounds as a unit of mass. But as there is gravity at its location the entire time it's in space, it most certainly has weight; the situation is nearly the exact same as it is for the rock, except the rock also has to contend with air resistance.

As far as knowing what the mass is - where the hell is the mass supposed to go? The mass = the mass you started with, minus urine dumps (fairly simple to determine the mass from the volume) and minus fuel burns (you'd think that they knew how much fuel is burned in x amount of seconds; at least to the nearest tenth of a pound. However, on the surface of the moon, they gathered samples. I'm going to bet that they didn't just guess on the mass/weight of those samples. Plus, they left stuff behind; I'm going to guess that someone had a pretty good idea what the mass/weight was of the stuff that was left behind.

 

[DirkGently1]

Inverse square law. The weight would decrease by this factor the further they travelled from the clutches of Earths Gravity, and of course increase again as they approached the Moon.

The other known quantities would be amount of fuel burned as well as jettisoned parts of the craft.

 

[uclabachelor]

It boils down to F = MA.

F = the thrust of the engine/booster which is always known, either from sensor measurements or from experimental data.

A = acceleration of the mass, which can be calculated from on board gyroscopes.


The mass is just F divided by A.

The weight depends on the gravitational bodies in space.