How much fuel did a saturn V burn before it lifted off.

[Brethern]

I read that the saturn V had a fuel efficiency of roughly 4.1 inches to a gallon. So naturally I got curious as to how much fuel it burned in the few seconds before it lifted off.

I then realized that there's no fuel efficiency calculator that goes down to inches So I'm forced to do this by hand that is where I need the help. According to this video

The main engine fires roughly 12 seconds before it movies. Going by that do we have enough info to calculate this?

PS I do know they mention 20 tonnes a second I'm assuming that's while moving Even if it is it's still a fun math exercise.

[KASASpace]

Well, how much fuel is used up per second per F-1 engine?

According to Wikipedia the fuel pump provided 58,560 L of fuel every minute.

So, let's divide 58,650 by 60:

977.5 L per second per engine.

Now, multiply times 5:

4887.5 L per second.

That's fairly close, but not exact.

EDIT: whoops, need to redo that........ and redone

EDIT 2: 4887.5 multiplied by 12 will give you what you want I suppose.

Edited April 18, 2014 by KASASpace

[Armchair Rocket Scientist]

I read that the saturn V had a fuel efficiency of roughly 4.1 inches to a gallon. So naturally I got curious as to how much fuel it burned in the few seconds before it lifted off.

I then realized that there's no fuel efficiency calculator that goes down to inches So I'm forced to do this by hand that is where I need the help. According to this video

The main engine fires roughly 12 seconds before it movies. Going by that do we have enough info to calculate this?

PS I do know they mention 20 tonnes a second I'm assuming that's while moving Even if it is it's still a fun math exercise.

Whoever told you that either didn't understand rockets or was trying to dumb it down for someone who didn't understand rockets.

Measuring a rocket's fuel efficiency in terms of inches per gallon is nonsensical: the fuel flow rate of a rocket stage is pretty much constant throughout the flight (excluding throttling down to reduce structural loads), but its speed changes enormously. If I have a rocket that burns 1000 L of fuel per second, and it's moving at 1 m/s, it will burn 1000 liters of fuel per meter. That same rocket moving at 1000 m/s only burns 1 liter of fuel per meter.

Even measuring in terms of "liters per m/s" is absurd, since the rockets' mass (and ISP if you're climbing out of the atmosphere) change over time. Each liter of fuel burned provides more dV than the last.

The best measure of a rocket engine's efficiency is ISP/exhaust velocity, while the best measurements of a launch vehicle's efficiency are payload fraction and cost/kg, usually measured to LEO.

[KASASpace]

He wanted to know how much fuel was burned before lifting off.

[Brethern]

Well, how much fuel is used up per second per F-1 engine?

According to Wikipedia the fuel pump provided 58,560 L of fuel every minute.

So, let's divide 58,650 by 60:

977.5 L per second per engine.

Now, multiply times 5:

4887.5 L per second.

That's fairly close, but not exact.

EDIT: whoops, need to redo that........ and redone

EDIT 2: 4887.5 multiplied by 12 will give you what you want I suppose.

That is a bit of fuel just to get the thing moving.

Whoever told you that either didn't understand rockets or was trying to dumb it down for someone who didn't understand rockets.

Measuring a rocket's fuel efficiency in terms of inches per gallon is nonsensical: the fuel flow rate of a rocket stage is pretty much constant throughout the flight (excluding throttling down to reduce structural loads), but its speed changes enormously. If I have a rocket that burns 1000 L of fuel per second, and it's moving at 1 m/s, it will burn 1000 liters of fuel per meter. That same rocket moving at 1000 m/s only burns 1 liter of fuel per meter.

Even measuring in terms of "liters per m/s" is absurd, since the rockets' mass (and ISP if you're climbing out of the atmosphere) change over time. Each liter of fuel burned provides more dV than the last.

The best measure of a rocket engine's efficiency is ISP/exhaust velocity, while the best measurements of a launch vehicle's efficiency are payload fraction and cost/kg, usually measured to LEO.

I'm fairly certain the 4.1 Was from them comparing it's fuel efficiency to the same scale that's used by other vehicles.

[KASASpace]

That is a bit of fuel just to get the thing moving.

Well, I guess it takes about 58,650 L of fuel over 12 seconds. (Not oxidizer, counting that, it would be quite a lot more)

So, the answer was right there, and all that math was useless.

[sgt_flyer]

Mmmh - according to this timeline : http://history.nasa.gov/SP-4029/Apollo_11i_Timeline.htm

the engines start order comes 9.2s before first motion. Remember that during that time : first, there 's the gaz generator activation, to make the turbopumps spin.it seems they achieve full speed in 7.3s after start command (engines thrust ok line)

So during that spool up time, the turbopumps are not pumping fuel at a constant flow rate

[Armchair Rocket Scientist]

I'm fairly certain the 4.1 Was from them comparing it's fuel efficiency to the same scale that's used by other vehicles.

The problem is, that scale is meant for vehicles which maintain a constant speed for long time periods with quick bursts of acceleration, e.g. cars and trucks on a freeway and most boats and airplanes. It is utterly meaningless for a vehicle which accelerates for 10 minutes and then coasts for days to years.

It's sort of like if I said my car engine burns half a gallon of fuel per minute. While this may be true when the engine is at full power, e.g. if I'm going from zero to 60 as fast as possible, the engine might only burn 1/20th of a gallon per minute while cruising at 60 mph. Just saying "1/2 gallon per minute" with no context is completely useless as a measure of the fuel efficiency of my car.

[Lukaszenko]

As Armchair Rocket Scientist implied, a rocket's miles per gallon efficiency starts at 0 and goes up to pretty much infinity. This makes me very curious during which portion of the rocket's flight was the "4.1 in/ gallon" figure averaged.

[Sirrobert]

I read that the saturn V had a fuel efficiency of roughly 4.1 inches to a gallon. So naturally I got curious as to how much fuel it burned in the few seconds before it lifted off.

I then realized that there's no fuel efficiency calculator that goes down to inches So I'm forced to do this by hand that is where I need the help. According to this video

The main engine fires roughly 12 seconds before it movies. Going by that do we have enough info to calculate this?

PS I do know they mention 20 tonnes a second I'm assuming that's while moving Even if it is it's still a fun math exercise.

Well if you messure in distance per vollume, and it moves no distance, than by that logic it'd use no vollume.

In other words, whatever it is you read, it's pritty stupid (not even counting the fact that they use imperial units for rocket science)

And offcourse what the rest already said

[StrandedonEarth]

4.1 in/gallon is probably the distance moved while the engines are burning. Coast phases while staging or between 3rd stage firings complicates things. According to the wiki, The first stage efficiency was just under 5in per US gallon, while nothing is listed for the upper stages, which should be higher because they are already at speed.

[Ramps]

I would disagree with most of these arguments. First work out the Force which is rate of change of momentum (remember that the momentum is comprised the instantaneous velocity multiplied by the rate of change of mass plus the mass multiplied by the rate of change of velocity). Integrate over a suitably small time frame and multiply by the distance travelled. This will be the work done or energy to move the rocket a distance x. The actual energy  supplied by burning the fuel is the mass of fuel used multiplied by the specific exothermic energy per unit mass in breaking and creating bonds in the chemical reaction. The efficiency is then 100x difference in Energy supplied by fuel - work done divided by energy supplied by burning said fuel

[wizzlebippi]

I remember reading somewhere that each of the Saturn V's 1st stage engines burns 2 tons of fuel and 1 ton of oxidizer per second.  If that's true, the fuel burn from the turbo pumps is likely trivial, and you only need to worry about the last few seconds before launch for engine start and vehicle stabilization. My guess is the rocket is 45-60 tons lighter by liftoff.

[GoSlash27]

I work it out to about 85.7 metric tonnes of kerosene and oxidizer, assuming from this video that the fuel starts to flow about 7 seconds prior to liftoff and the turbopumps take about a second to get to full flow.

The maths:

assuming thrust at sea level is 34 MN and Isp is 263s,

mass flow rate= 34x10⁶/(9.81x263)= 13.2 Mg/sec

Assuming 6.5sec full flow, that's 13.2x10⁶ x 6.5 = 85.7 tonnes. this would convert to 189,000 lbs or 94.5 tons.

Best,
-Slashy

 

Edited February 7, 2016 by GoSlash27

[SgtSomeone]

2 hours ago, wizzlebippi said:

My guess is the rocket is 45-60 tons lighter by liftoff.

I was under the impression that rockets have fuel lines via the stabilizing tower (similar to how KSP has electrical supply in the launch towers), which would mean the rocket would still be full at liftoff. I mean, why would you design a rocket that is forced to carry an empty 45k L fuel tank to orbit (or separation) when you could decouple that tank on launch?

[DerekL1963]

22 minutes ago, SgtSomeone said:

I was under the impression that rockets have fuel lines via the stabilizing tower (similar to how KSP has electrical supply in the launch towers), which would mean the rocket would still be full at liftoff. I mean, why would you design a rocket that is forced to carry an empty 45k L fuel tank to orbit (or separation) when you could decouple that tank on launch?

They don't - because ground based pumps and reasonable sized umbilical connection can't deliver sufficient flow.   And, as far as weight goes, the bulk of the stage's weight is in the engines and thrust structure not tankage.   A meter or two of extra tankage isn't quite lost in the noise, but close.