Math unit conversion question

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The Dark
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Math unit conversion question

Post by The Dark » 2017-10-11 08:44pm

In comparing two tables of rocket engines, one lists fuel consumption in grams per kilonewton second (g/kn*s) while the other is in tonnes per tonne-hour (Mg/Mg*h). I think I've figured out the conversion between the two, but it's been a while since I've done anything physics-related, so could someone more up-to-date check my math below?

Starting in g/kn*s:

There are 1,000,000 grams per megagram (tonne), so the numerator will be multiplied by .000001.
There are 9,806.65 (approximately) kilonewtons per megagram, and 3600 seconds per hour.
Multiplying 9,806.65 by 3600, the denominator will be multiplied by 35,303,940.
The effective conversion is .000001/35,303,940.
Multiplying both numerator and denominator by 1,000,000, the conversion becomes 1/35,303,940,000,000 (3.5039x10^13)
Thus, taking fuel consumption in g/kn*s and dividing it by 3.5039x10^13 gives fuel consumption in Mg/Mg*h

Does this look correct, or have I made an error in breaking this down and doing the conversion step-by-step?
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Re: Math unit conversion question

Post by SpottedKitty » 2017-10-12 12:01am

Are these tables online anywhere? I'm not sure if the two can be compared effectively without a bit more massaging — "kilonewtons" is a unit of force, and "tonnes" is a measure of mass (not weight). Back in school, our Physics teacher told us not to confuse the two, or else the ghosts of Goddard and Tsiolkovsky would slap us upside the back of the head with a slide rule.

This is trickier than I thought it would be at first; my Google searches keep pointing me towards either the Rocket Equation, which I don't think applies directly, or articles on model rockets, which I'm fairly sure don't apply (not for the obvious reason, but because they use tiny solid motors).
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Re: Math unit conversion question

Post by houser2112 » 2017-10-12 08:26am

SpottedKitty wrote:
2017-10-12 12:01am
I'm not sure if the two can be compared effectively without a bit more massaging — "kilonewtons" is a unit of force, and "tonnes" is a measure of mass (not weight). Back in school, our Physics teacher told us not to confuse the two, or else the ghosts of Goddard and Tsiolkovsky would slap us upside the back of the head with a slide rule.
Force and mass are related through the acceleration of the body. You could assume, under normal circumstances for bodies at rest, that acceleration is g. Since we're talking about moving bodies, I'm not sure g is the appropriate value in the first place, and since we're talking about rockets, which tend to move in ways that g isn't even constant for the duration, it likely applies even less.

Which is a very roundabout way of saying "I'm not sure if the two can be compared effectively without a bit more massaging". :)

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Re: Math unit conversion question

Post by The Dark » 2017-10-12 06:28pm

SpottedKitty wrote:
2017-10-12 12:01am
Are these tables online anywhere? I'm not sure if the two can be compared effectively without a bit more massaging — "kilonewtons" is a unit of force, and "tonnes" is a measure of mass (not weight). Back in school, our Physics teacher told us not to confuse the two, or else the ghosts of Goddard and Tsiolkovsky would slap us upside the back of the head with a slide rule.
Yeah, my numbers were coming out wonky, so I suspected I had a units issue.

One of the tables is the Engine List from Atomic Rockets.

The other is from a game, so it's not online (AFAIK). To be honest, this is partially to see how outrageous the game's engines are. After re-reading, it says "thrust is measured not in Gs, but in tonnes of thrust (the thrust necessary to give 1 tonne of mass an acceleration of 1G)." That was something I had missed in my first reading. The fuel consumption is in tonnes of fuel per tonne of thrust per hour.
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Re: Math unit conversion question

Post by SpottedKitty » 2017-10-13 12:20am

Hmm... I wouldn't (quite!) call that game setup "outrageous", more an unconventional use of standard terms. I'm even less sure now than I was to begin with that the two tables are compatible — the game table sounds at least self-consistent and good enough for game use, but I don't think anyone working for SpaceX would want to use it. :wink:
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Re: Math unit conversion question

Post by The Dark » 2017-10-13 01:45am

I think it can work. A newton is the equivalent to the force acting on 0.102 kilograms at 1 g, so a kilonewton should be equivalent to 1020 kilograms at 1 g, or 1.02 tonnes at 1 g; that is to say that by the definition used in the second table, it's 1.02 tonnes of thrust (since that table defines a tonne of thrust as the force needed to accelerate 1 tonne at 1 g). Plugging that in to the first equation means it's calculating grams of fuel per 1.02 tonnes of thrust per second, and now we need to convert grams per second to tonnes per hour to alter the other two units.

277.78 grams per second equals 1 tonne per hour, and by multiplying the two divisors together (277.78 for g/s to Mg/h and 1.02 for kn to Mg*g), taking a fuel consumption number from the first table and dividing it by 283.3356 should give me fuel consumption on the second table.

One outcome (and something I suspected) is that the game uses inefficient rockets as their examples, since they have a 1970s-era rocket using 4.5 tonnes of propellant (fuel plus oxidizer) per tonne of thrust per hour. The F-1 engine from the Saturn V burned about 1.8 tonnes of propellant per tonne of thrust per hour.
Stanley Hauerwas wrote:[W]hy is it that no one is angry at the inequality of income in this country? I mean, the inequality of income is unbelievable. Unbelievable. Why isn’t that ever an issue of politics? Because you don’t live in a democracy. You live in a plutocracy. Money rules.
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