How much rocket fuel is burned in the first mile/kilometer?

[vjk2]

Take a typical single-stage rocket that reaches low Earth orbit (that's around 2000 km).

How much fuel is burnt just to get the thing a foot off the ground? Or a kilometer or a mile? 10%?

 

[Astronuc]

Take a typical single-stage rocket that reaches low Earth orbit (that's around 2000 km).

How much fuel is burnt just to get the thing a foot off the ground? Or a kilometer or a mile? 10%?

According to this site - http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Single-stage-to-orbit.html - "No Earth-launched SSTO launch vehicles have ever been constructed." Even the Space Shuttle uses booster rockets to lift the external tank with the shuttle. Most satellites are delivered with mutltistage launch vehicles.

To put things into perspective - http://www.nasa.gov/mission_pages/station/expeditions/expedition30/tryanny.html

http://www.braeunig.us/space/propel.htm

 

[vjk2]

Oops.

Okay, repurpose the question. For the space shuttle and Saturn rockets, how much fuel is needed to get off the ground? A km/mile?

HOw much is saved by ejecting spent stages?

 

[bigfooted]

You can calculate it yourself:
http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
from this page:
A hypothetical example from the wiki page:

Assume an exhaust velocity of 4.5 km/s and a \Delta v of 9.7 km/s (Earth to LEO).

Single stage to orbit rocket: 1-e^{-9.7/4.5} = 0.884, therefore 88.4% of the initial total mass has to be propellant. The remaining 11.6% is for the engines, the tank, and the payload. In the case of a space shuttle, it would also include the orbiter.

 

[Enthalpy]

Single stage launchers to orbit have not been done. Performance would suffice easily since several decades ago, but an SSTO wouldn't be very efficient. Additionally, it would need an engine that throttles much stronger than they presently do, so the acceleration remains bearable at the end, adn preferably that is efficient in the atmosphere and in vacuum - but if using two engines with different thrust, why throw them away both at the end instead of successively?

So SSTO makes sense mainly if the launcher is reusable - and this can be done easily with two stages.

Also, most launchers want to go to GTO or GSO, not LEO, and then a single stage is much harder.

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Quite a bit performance is lost at the beginning. This would improve if accelerating stronger, BUT
- A stronger engine with the same nozzle diameter is less efficient
- An engine as strong that lifts more propellant delivers more payload for nearly the same cost.

As a result, launchers lift-off at 1+0.3G to sometimes 1+0.6G, though Saturn V had only 1+0.17G.

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If starting at 1+0.3G as is common, the first km is reached after 26s, it costs 336m/s performance while the launcher has only 77m/s there, so the weak acceleration wastes 259m/s performance in the first km - over some 9500m/s performance to reach low orbit.

Atmospheric drag is very small on medium or big launchers. This would enable a stronger acceleration as well, but faster through the air means a stronger stress on the launcher.

When evaluating the gravity losses on a launcher, one should not compare the performance with the orbital speed! The altitude needs some performance as well, with an ideal Hohmann transfer to circular 400km consuming about 1000m/s over the orbital speed.

Neither are the estimated 259m/s what launch from an aeroplane or mountain would bring.

Put together, an idealized launch scenario would save less than 1000m/s performance or just 1/3 of the start mass - which tells why most launchers are desperately classical. Earbreathing would bring more only if used at an important fraction of the 9500m/s, which is not even considered presently.