# Re: [Propulsion] Minimum Isp

```Glad to see new activity here.

I did a lot of independent research and calculations on this stuff a
few years back, and my conclusion was basically that the propulsion
team should think about designing one stage of a hypothetical three
stage rocket - that is, a stage with a delta-v of ~3.2km/s when the
payload mass is based on the non-propulsion components of previous
launch vehicles. Achieving such a thing would go a long way toward
gaining credibility, and it'd make one hell of a sounding rocket on
its own. A really conservative rough estimate, assuming 50% kinetic
energy lost due to drag effects, still puts the rocket at more than
200km altitude.```
```
An actual three stage orbital LV would benefit from not having each
stage contribute an identical amount of delta-v. Specifically, it
makes sense for the first stage to be very high acceleration for a
short amount of time, and the last stage to be a longer, slower, high-
efficiency burn. The reason for this is that high acceleration is
desirable when lifting off vertically because you're losing 1 g just
to overcome gravity. However, if your mass ratio for that stage mo/mf
is, say, 0.5, this means your total accelerating mass is going to
drop in half over the burn, and in the absence of throttling (a
recommended absence) your acceleration is going to be twice as high.
Therefore the limiting factor on the delta-v contributed by any stage
is that the initial acceleration must be great enough that the 1g
loss is not significant, but the final acceleration must not tear the
vehicle apart.

This leads to a more realistic estimate of perhaps 2 to 2.5km/s delta-
v from the first stage, as a design goal. This is doable with an
exhaust velocity of 2500m/s and a fuel/total mass ratio of 63%. Still
pretty technically challenging, but within reason. Keep the design as
simple as possible, consider doing some test launches without the
full avionics and recovery package - just having the nose cone pop
off and deploy a streamer to spoil the aerodynamics is a lot more
reliable than a parachute recovery system deployed by a computer
running Java. By now it should be obvious that the Shuttle is the
opposite of good design practices in terms of reliability,
infrastructure required to launch, frequency of launch, &c.

Some things to consider.

Richard Campbell

On 25 Oct 2007, at 06:53, rq17zt wrote:

> Hey all,
>
> Since Andrew was talking about re-starting the propulsion list
> recently, here's post ;)
>
> ---
>
> Tom and i were discussing scaling laws for Isp at the
> Wed. meeting. I'll give a summary, but this is just from my memory, so
> receive it with some skepticism.
>
> As a simple 1st approach to designing a motor for orbit, we estimate
> the mission requirement as a vehicle capable of achieving a certain
> minimum delta-V. Meaning the relative speed the vehicle would achieve
> absent losses such as gravity and air friction. For our 1st guess we
> selected the minimum delta-V as ~9 km/s, around 20% more than the
> orbital velocity, which is about 7.6 km/s.
>
> (I went back and looked up our old requirement estimate,
>  it was 9.46 km/s.)
>
> Delta-V can be computed in terms of the mass ratio and propellant
> exhaust velocity as
>
>   1) delta-V = c * Log[m0 / mf]
>
> Where (c) is the propellant exhaust velocity, (m0) is the initial
> vehicle mass, and (mf) is the final vehicle mass at burn out.
>
> For the record,
>
>   2) c = gee * Isp
>
> Where (Isp) is the specific impulse, defined as Thrust/(mass flow
> rate), and (gee) is the Earth's gravity, which i believe by convention
> is assumed to be 9.8066 m/s^2. For calculations never use Isp
> directly, always use exhaust velocity.
>
> ---
>
> The important thing about the 1st equation is that there is an
> exponential relationship between (c) and the fraction of the initial
> vehicle mass that must be propellant. Further, for a given structural
> technology there is an upper limit on how large the propellant
> fraction can be. Therefore given the structural technology there is a
> minimum Isp needed to reach orbit.
>
> When talking with Tom at the meeting i forgot that all this applies to
> single stage vehicles. Staging improves the situation somewhat, so we
> should take that into account in our calculations.
>
> ---
>
> In the rocket biz there is a standard way of expressing the propellant
> fraction etc.
>
>   (mL) is the mass of the payload
>   (mp) the propellant mass
>   (md) is the dead 'weight' (Useless stuff like motors and tanks,
> etc. ;)
>
> I'm not sure how well it works, but it's common to attempt to separate
> the effects of payload mass from propellant and vehicle structure,
> which motivates the definition of the "propellant mass fraction"
>
>   Lp === mp / (mp + md)
>
> Eq(1) can be rewritten in terms of (Lp)
>
>                       [   Lp mL + mp    ]
>   3) delta-V = c * Log[-----------------]
>                       [Lp mL + (1-Lp) mp]
>
>
> ------
>
> It would be nice if as part of exploring propellants we could get this
> info up on the Wiki in a semi-polished form.
>
> ------
>
> The rest of this info is taken verbatim from my old notes, much of
> which were based on the talk we got from Ranier Anacker.
>
> Typical propellant exhaust velocities: [m/s]
>   Hydrogen + Oxygen       3700, 4500
>   Kerosene + Oxygen       2700, 2800
>   Gasoline + Oxygen       2600, 2700
>   Alcohol  + Oxygen       2500, 2700
>   Shuttle SRBs            2500, 2600
>   Most Solids             2200, 2500
>
> "Realistic Lp values are between 0.7 and 0.9."
>
> Mass fraction of real rockets:
>  Vehicle                mp[kg]     md[kg]     Lp        mL[kg]
>   V2 (1945)              8482       3082       0.7335    1000
>
>   Shuttle SRB            502700     81900      0.8599    -
>   Shuttle External Tank  703100     35000      0.9526    -
>   Shuttle E.T.+Orbiter   703100     178300     0.7977    -
>   Shuttle (1995)         1708500    342100     0.8332    13000
>
>   DeltaII (1995)         207706     19359      0.9147    2000-5000
>   DeltaIII (2000)        262749     27468      0.9054    8000
>
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>

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