Nerdy calculations

Update:

This is now included in the latest series I'm writing.  It's about the Hunter Gas Gun used as a propulsive device for space.  Part Five of the Series.  Part Four is here.

How much energy in a gallon of gasoline?  Answer: 1.3 * 10 ⁸ Joules.

The reason I mention it is that a gallon of hydrogen is said to be comparable.  Also, that it take 40% of the energy content of hydrogen to put it into liquid form.  That's an astounding amount of energy.  A Joule is about a Watt, by the way.  There are 3.79 liters in a gallon.  So, let's approximate how much energy is required to liquify 1 liter of hydrogen.   It is:   .40 times 1.3 * 10 ⁸  divided by 3.79 equals 0.137 * 10 ⁸  Joules or about 10% of a gallon of gasoline.

Why is this important?  Well, I want to do a thought experiment here in order to see if an idea might have some merit.  That's using the hydrogen gas in a hydrogen gas gun for a spacecraft's propulsion.

Here's the point.  There's already a lot of energy in the liquid hydrogen.  Just one liter has 1.37 * 10 ⁷  Joules ( watts ) in it which could do work before you do anything else to it.  That's about 13 megawatts for those of you in Rio Linda.

I did another nerdy calculation by figuring out how many atmospheres of pressure it takes to get to liquid hydrogen.  In other words, at standard temperature and pressure, there 2 grams of hydrogen for every 22.4 liters of volume.  If you take 1 liter of liquid hydrogen and heat it up to room temperature, you will get something like 700 atmospheres of pressure.

The pressure is what can do your work for you.  Like taking an ice cube that weighs about 10 grams and accelerating it to 2.5 km/sec.  Looks like it will give you about 31250 Joules of energy to that ice cube.

What does that do for you?  Well, that 31 kilowatts of power right there.  One kilowatt  = 1.34102209 horsepower.  One horsepower equals 550 lb-ft.  That would equal 22864 lb-ft of kinetic energy which can be used as thrust to propel a spacecraft.

All that from one ice cube?

No.  You'd have to do it every second in order to do some useful work.  A typical rocket may fire for a couple minutes or more.   You would need  a rapid firing capability of at least once per second for that long in order to transmit some respectable delta-v.

The space shuttle took 8 minutes to get to orbit.  Thats 480 seconds.  So, for about 10 pounds worth of ice, you could get 22k lbs of thrust for eight minutes.


I don't know if you'll even use 1 liter of liquid hydrogen for each shot, but I could be wrong about that.  It has to traverse a lot of tubing.  If you used about 1 liter for each shot, for 480 shots, it would take 480 liters.

Not bad.  It won't get you much velocity though.

Well, that's enough for now.