🚀 go-pugleaf

In article <PAULI.RAMO.93Jan24190410@vipunen.hut.fi> Pauli.Ramo@hut.fi writes:

>In article <74006@cup.portal.com> BrianT@cup.portal.com (Brian Stuart Thorn)
>
>The *thrust* is not a problem, after getting to LEO. If you have less
>thrust, it only takes a little longer to get to the Moon. In fact, you
>could make both TLI and LOI with only one OMS (or even RCS) engine, if
>you had enough fuel to it and it lasted a long continuous firing. The
>problem is the amount of fuel needed.
>
>There is a simple equation to calculate the amount of velocity change
>for a given amount of fuel and mass of vehicle:
>
>        dv = ln (m/m0) * I
>
>where
>dv = velocity change
>m  = initial mass (with full tanks)
>m0 = mass without fuel (empty tanks & payload)
>I  = the impulse of the engine used
>
>With chemical rockets, I is some thousands of m/s. For example, the impulse
>of SSME is about 4400 m/s. With SRB's it is lower.
>
>For a complete trip to moon and back, you must sum the velocity changes 
>needed in it's various parts together and use that to calculate your 
>fuel requirements. Unfortunately, I don't have the exact requirements
>for TLI, LOI, TEI and EOI on hand (maybe someone can help me here), but
>even LEO requires a total velocity change in the order of 9000 m/s.
>
>Thus, to only get to LEO with a single stage booster equipped with SSME's,
>you had to have the mass ratio of about 7.73:1. That means that of the
>initial mass of the vehicle, 87% had to be used as fuel just to get to
>LEO, and the remaining 13% would include all the tanks and engines for
>the fuel.
>
>If someone has the velocity change requirements for the rest of our trip
>to moon, we can continue this little number game.
>
>        Pauli
>--
>Disclaimer fault - lawyers dumped
>

Your equation is too simplistic - it only really applies either in the
absence of gravity, or if the velocity change occurs instantaneously
(ie, an "impulse").  If the fuel is burned over a finite time, you
have to take into account the losses due to gravity and (if in atmosphere)
friction.

For example, if you have a rocket on a launch pad, and that rocket
produces <1g of acceleration, it can burn all its fuel, but its velocity
will stay at zero!

Best wishes,

Chris
-- 
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| Chris Marriott                           | chris@chrism.demon.co.uk    |
| Warrington, UK                           | BIX: cmarriott              |
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