DeltaV, Exhaust Velocity, and Particle Mass?

I'm a layman discovering the intricacies of space flight.

I understand that the equations for DeltaV denote it as a sole function
of mass ratio and engine exhaust velocity, but why doesn't exhaust
particle mass factor into the equations as well? Shouldn't a exhaust
of "heavier" particles at the same exhaust velocity produce a greater
velocity gain to the ship?

I guess I'm looking at it from a conservation of linear momentum sort
of thing, where momentum gained by the ship should equal the momentum
induced in the particles so heavier particles at the same velocity
would incur great momentum gains and thus greater deltaV...... So a
ship with a mass ratio of 2, exhaust velocity of 10km/s that uses Ar
for exhaust, would have a greater overall deltaV than a ship with the
same mass ratio and same exhaust velocity that uses hydrogen...(that
is, of course, assuming that an equal exhaust velocities can be
obtained with heavier particles which I know isn't usually the case)

Can anyone explain to me if I'm mistaken and why... why don't heavy
particles = more deltaV

Benjamin B wrote:
I'm a layman discovering the intricacies of space flight.

I understand that the equations for DeltaV denote it as a sole function
of mass ratio and engine exhaust velocity, but why doesn't exhaust
particle mass factor into the equations as well? Shouldn't a exhaust
of "heavier" particles at the same exhaust velocity produce a greater
velocity gain to the ship?

No, and it's backwards from that.

Can anyone explain to me if I'm mistaken and why... why don't heavy
particles = more deltaV

Consider a given mass of exhaust gas, expanding through a nozzle, to a
given speed (which will depend on initial temperature).

It starts out with enough thermal energy to produce a stream of gas
going at speed v, linearly away from the nozzle (pretty much).

The gas starts at rest (WRT the rocket), and accellerates to V, so it
now has a momentum of m*v.
This change in momentum of course can't come from nowhere, and the
rocket is pushed one way, as the gas goes the other.

It doesn't matter what the gas is, just that it's got a given mass per
unit time, and accellerates.

However.

In real life, for a gas heated to a given temperature (by combustion,
friction, nuclear reaction or whatever), the average velocity of the
molecules of the gas before they go through the nozzle is much higher
for lighter molecules.
This means that after they go through the nozzle, they go faster, for a
given initial temperature.

And, if they are going faster, for a given mass of gas, they have more
momentum, so more momentum is transferred to the rocket.

"Benjamin B" wrote in message oups.com...
I'm a layman discovering the intricacies of space flight.

I understand that the equations for DeltaV denote it as a sole function
of mass ratio and engine exhaust velocity, but why doesn't exhaust
particle mass factor into the equations as well? Shouldn't a exhaust
of "heavier" particles at the same exhaust velocity produce a greater
velocity gain to the ship?

I guess I'm looking at it from a conservation of linear momentum sort
of thing, where momentum gained by the ship should equal the momentum
induced in the particles so heavier particles at the same velocity
would incur great momentum gains and thus greater deltaV...... So a
ship with a mass ratio of 2, exhaust velocity of 10km/s that uses Ar
for exhaust, would have a greater overall deltaV than a ship with the
same mass ratio and same exhaust velocity that uses hydrogen...(that
is, of course, assuming that an equal exhaust velocities can be
obtained with heavier particles which I know isn't usually the case)

Can anyone explain to me if I'm mistaken and why... why don't heavy
particles = more deltaV

Holding exhaust velocity constant, you DO get more deltaV per particle
from larger particles. But you get identical deltaV per Kg of exhaust.
As you note, the other factor besides exhaust velocity is mass ratio,
not particle-count ratio.

Well, if you end up pushing 10 tons of mass out the back of a rocket
it's 10 tons if it's of light materials or heavy materials, so m*v is
the same. So picking a mass ratio of 2 fixes the mass that will come out
of the rocket, albeit with many little particles from the light material
and few large particles for the heavier material.

Above that, as you say the specific energy and hence the exhaust
velocity tend to be lower for the heavier reactions.

James

"Benjamin B" wrote in message
oups.com...
I'm a layman discovering the intricacies of space flight.

I understand that the equations for DeltaV denote it as a sole function
of mass ratio and engine exhaust velocity, but why doesn't exhaust
particle mass factor into the equations as well? Shouldn't a exhaust
of "heavier" particles at the same exhaust velocity produce a greater
velocity gain to the ship?

I guess I'm looking at it from a conservation of linear momentum sort
of thing, where momentum gained by the ship should equal the momentum
induced in the particles so heavier particles at the same velocity
would incur great momentum gains and thus greater deltaV...... So a
ship with a mass ratio of 2, exhaust velocity of 10km/s that uses Ar
for exhaust, would have a greater overall deltaV than a ship with the
same mass ratio and same exhaust velocity that uses hydrogen...(that
is, of course, assuming that an equal exhaust velocities can be
obtained with heavier particles which I know isn't usually the case)

Can anyone explain to me if I'm mistaken and why... why don't heavy
particles = more deltaV

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Benjamin B wrote:
So a
ship with a mass ratio of 2, exhaust velocity of 10km/s that uses Ar
for exhaust, would have a greater overall deltaV than a ship with the
same mass ratio and same exhaust velocity that uses hydrogen...

What's heavier, a tonne of feathers or a tonne of bricks?

- --
+- David Given --McQ-+ "`Aplysia californica' is your taxonomic
| | nomenclature.
| ) | A slug, by any other name, is still a slug by
+- www.cowlark.com --+ nature." --- drushel on a.f.c

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On Sat, 25 Feb 2006, in sci.space.tech,
Benjamin B said:

Can anyone explain to me if I'm mistaken and why... why don't heavy
particles = more deltaV

Think of a tank full of particles. If the tank contains a ton of them
and the particles are a picogram each, there's 10^18 of them in the
tank. If they are a nanogram each, then each particle will have 1,000
times the momentum, but there will only be 10^15 of them in a ton, so it
all works out. The mass is taken care of in the "mass ratio" term, so
you don't have to worry about it in the exhaust.

--
Del Cotter
NB Personal replies to this post will
send email to
Please send your email to del2 instead

You are partially right. Thrust is directly proportional to the amount
of mass ejected per time unit (and to the velocity of that mass, of
course). So, if we are assuming same volume (flow) and same velocity,
yes, the higher the density, the higher the thrust.

Of course, if you only limit the velocity (same velocity), you can
achieve the same thrust for different densities just adjusting the
exhaust area (volume, or flow).

And finally, as you indirectly remark, it depends on the nature of the
propellant; its internal energy, or its "capability to provide thrust".
This is measured through the "specific impulse" (Isp) of the
propellant, what is defined as the time that a propellant mass of 1 kg
is able to provide 1 N of thrust (in IS units; analog for imperial
ones). The higher the Isp, the less amount of propellant needed to
provide the same thrust (more efficiency).

Regards,

Javier Casado
Madrid, Spain
http://es.geocities.com/fjcasadop