[AR] Re: Rocket thrust change with altitude, RPA
- From: Alexander Ponomarenko <contact@xxxxxxx>
- To: arocket@xxxxxxxxxxxxx
- Date: Fri, 28 Oct 2016 07:59:23 +0200
As Pe increases higher than Pa (under expansion), Ve drops and to a
lesser
extent Ae drops too thereby reducing F
So, you are changing both Ve and Ae.
But this does not correspond to your own statement "*the engine* will be
at optimal performance (for the operating conditions) only when Pe=Pa",
because as soon as you change Ve or Ae it is probably not the same
engine (or at least not the same operational configuration).
why does Pe=Pa produce more thrust than Pe>Pa for the same mass flow
and throat area
As Pe increases higher than Pa, Ve drops and to a lesser extent Ae
drops too
As Pe reduces lower than Pa (over expansion) Ve increases,
Actually, you are comparing *different* engines with different values of
Ve and Ae, because for the *same* engine neither Ve nor Ae is changed
with the altitude (as long as we don't have the nozzle with variable
geometry).
But if you consider *the same* engine ({pc, Mdot, Ae}=const) at
different ambient conditions, you will see that the lower Pa the better
engine performance (that is, thrust and Isp is higher).
Regards,
Alexander
On 10/28/2016 07:12 AM, Troy Prideaux wrote:
Just to clear this up a bit more:
F = q × Ve + (Pe - Pa) × Ae
where F = Thrust
q = Propellant mass flow rate
Ve = Velocity of exhaust gases
Pe = Pressure at nozzle exit
Pa = Ambient pressure
Ae = Area of nozzle exit
So, why does Pe=Pa produce more thrust than Pe>Pa for the same mass flow and
throat area:
(1) Ve is inversely proportional to Pe
Due to Ve = SQRT((2 * k / (k - 1)) * (R' * Tc / M) * (1 - (Pe / Pc)(k-1)/k))
And
(2) Ae must also drop as Pe increases
Ae =
At/(((k+1)/2)^(1/(k-1))*(Pe/Pc)^(1/k)*SQRT((((k+1)/(k-1)))*((1-((Pe/Pc)^((k-1)/k))))))
So, for F = q × Ve + (Pe - Pa) × Ae
As Pe increases higher than Pa (under expansion), Ve drops and to a lesser
extent Ae drops too thereby reducing F
As Pe reduces lower than Pa (over expansion) Ve increases, but pressure
thrust reduces more as it goes negative and coz that negative number is
multiplied with Ae which itself increases, the resultant negative is more
than the increase in Ve alone.
Troy
Ed (Kelleher),
The confusion here is that you're specifically looking at the pressure
thrust side of the equation what relates specifically to pressure imbalances
and yes, it is true that for an under expanded nozzle, the pressure thrust
will be higher than for an optimally expanded nozzle. However, the momentum
thrust will be reduced even more because the velocity component of that also
accounts for the pressure balance between Pc,Pe - in particular this part of
the momentum thrust equation : "(1 - (Pe / Pc)^(k-1)/k)" As you can see, as
you increase Pe, the contribution from this part is lower as it's being
subtracted from 1. In the end, this influence overrides the pressure thrust
contribution.
Here is probably the best explanation you're ever likely to see:
http://www.braeunig.us/space/sup1.htm
Troy.
Other related posts:
- » [AR] Rocket thrust change with altitude, RPA- Ed Kelleher
- » [AR] Re: Rocket thrust change with altitude, RPA- Ed LeBouthillier
- » [AR] Re: Rocket thrust change with altitude, RPA- Manuel Schleiffelder
- » [AR] Re: Rocket thrust change with altitude, RPA- Alexander Ponomarenko
- » [AR] Re: Rocket thrust change with altitude, RPA- Alexander Ponomarenko
- » [AR] Re: Rocket thrust change with altitude, RPA- Troy Prideaux
- » [AR] Re: Rocket thrust change with altitude, RPA - Alexander Ponomarenko
- » [AR] Re: Rocket thrust change with altitude, RPA- Norman Yarvin
- » [AR] Re: Rocket thrust change with altitude, RPA- Ed Kelleher
- » [AR] Re: Rocket thrust change with altitude, RPA- Henry Spencer
- » [AR] Re: Rocket thrust change with altitude, RPA- Norman Yarvin
- » [AR] Re: Rocket thrust change with altitude, RPA- Alexander Ponomarenko
- » [AR] Re: Rocket thrust change with altitude, RPA- Ian Woollard
- » [AR] Re: Rocket thrust change with altitude, RPA- Norman Yarvin
- » [AR] Re: Rocket thrust change with altitude, RPA- Troy Prideaux
- » [AR] Re: Rocket thrust change with altitude, RPA- John Dom
- » [AR] Re: Rocket thrust change with altitude, RPA- Norman Yarvin
- » [AR] Re: Rocket thrust change with altitude, RPA- Henry Spencer