Rockets for Dummies
The Physics Behind Rockets
By:John Berrigan, berriganj@hdsb.ca
For:OAPT 2009, May 29th
Why space?
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Cool factor.
Canadian on ISS for 6 months…arrived today.
RMC contributions.
Who applied for the canadian Astronaut Program?
International competitions/milestones.
X-prizes
Return to moon
Why Rockets?
• Cool Factor
• In the news
• Lots of current applications
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(lots of great videos at the sites, be sure to check them out)
Sub orbital tourism
Spacex (go to their website for cool videos)
Virgin galactic
Xcor
Rocket Racing League
Armadillo (“doom” game creators rocket)
Blue Horizon (“Amazon” owner)
To name a few
The Physics Needed
• Conservation of momentum
• Impulse
• Newtons Laws
– A GREAT Application for Newton’s 3rd law
• Electrostatics
• Magnetism
Conservation of Momentum
• From Newtons 3rd law
(“prime” value represents the final value)
FAB = - FBA
mAaA = - mBaB
mAΔVA/ΔtA = - mBΔVB /ΔtB but Δt’s are the same so they cancel out
mA(VA’ – VA) = - mB(VB’ – VB)
Rearranging,
mAVA+ mBVB = mAVA’+ mBVB’
pT = pT’
Total Momentum Before = Total Momentum After
Impulse
From Newton’s 2nd Law
FA = mAaA
FA = mAΔVA/ΔtA
Rearranging
FAΔtA = mAΔVA
FAΔtA = mA(VA’ –VA)
FAΔtA = mAVA’ – mAVA
FAΔtA = pA’ –pA
FAΔtA = ΔpA
Thrust equation
Impulse = FthrustΔt = Δp
Fthrust Δt = Δ(mV)
Some calculus
FthrustΔt = (Δm)V + m(ΔV)
From the frame of reference of the rocket engine, it is losing
mass and the velocity that it is throwing the mass out is
constant, so….
Δm isn’t zero and ΔV is zero
FthrustΔt = (Δm)V
Or
Fthrust = (Δm/Δt)V
Implications
What does the equation Fthrust = (Δm/Δt)V
imply?
To get the largest thrust you either want to
throw the mass as fast as possible (large V),
or throw out as much mass as possible in
the shortest amount of time (large Δm/Δt).
What is better?
Conservation of momentum
A 12 kg frictionless cart has 8 kg of “fuel” to
be thrown off the cart. The fuel can be
thrown off at 10 m/s relative to the cart.
8 kg
8 kg
12 kg
pT = mv
= 20(0)
=0
v12
pT = pT’
0 = 20v12 – 80
V12 = 4
V12 - 10
12 kg
pT’ = mv12 + mv8
= 12v12 + 8(v12-10)
= 20v12 - 80
What if mass is thrown in 2 parts? In two 4
kg chunks!
4
4
4
12 kg
v16
pT = mv
= 20(0)
=0
4
V16 - 10
12 kg
pT’ = mv16 + mv4
= 16v16 + 4(v16-10)
= 20v16 - 40
pT = pT’
0 = 20v16 – 40
V16 = 2
4 kg
4
12 kg
pT = mv
= 16(2)
= 32
v12
pT = pT’
32 = 16v12 – 40
V12 = 72/16
V12 = 4.5
V12 - 10
12 kg
pT’ = mv12 + mv4
= 12v12 + 4(v12-10)
= 16v12 - 40
So final velocity is faster if done in smaller
parts!!
What are the implications of this?
What is the smallest mass you can practically throw
off?
1 g? 0.01 g? 1 ng??
Is an electron possible?
Problem is there is a lot of mass left behind…
So real answer is an atom.
So the most efficient engine throws out one atom at a
time.
This is called an ion engine!!
So What to do with this Info?
There are always pros and cons when doing things.
For throwing a smaller amount of mass out:
Pros:
• you get much higher final velocity.
Cons:
• Very low thrust.
• Imagine throwing out one atom at a time..not
much force can be generated.
For Throwing lots of mass out at a time:
Pro:
• Higher thrust
Con:
• Slower final velocity
If you want to get out of a “gravity well”. You
want high thrust so you throw lots of mass
out at a time.
If you want to go faster, low thrust is fine.
Efficiency is key for this!!!
Specific Impulse (Isp)
We need to introduce a way to deal with how
efficient a rocket engine design is.
Specific impulse is a way to do this.
By definition,
Isp is the length of time 1 kg of fuel can
produce 9.8 N of thrust.
Isp
Isp actually makes some sense.
If one engine has an Isp of 3 s and the other
300 s which one is better?
If it takes 3 s to produce the 9.8 N of thrust
you are using the fuel very quickly.
If it takes 300 s to produce the 9.8 N of thrust,
you are taking a long time to use the mass
and it is therefore much more efficient.
Applications
How do we use the Isp formula and thrust formulas?
Example
If a rocket engine has an Isp of 300 s, how much fuel
must be used to produce 1000N of thrust?
Isp
FΔt = Δm(v)
9.8(300) = 1v
V = 2940 m/s
Thrust
F = (Δm/Δt)(v)
1000 = (Δm/Δt)(2940)
Δm/Δt = 0.340 kg/s
Combining formulas
If we combine the thrust and ISP formulas we
get the equation,
Fthrust = (Δm/Δt)(Isp*9.8)
So why don’t we use high ISP rocket engines all the
time?
Has to do with the physics and thrust to mass ratio.
Rocket Engine design
Three main parts
1. You need something the “throw”. Which
is the fuel.
2. You need Energy. Used to throw the fuel.
3. You need some sort of nozzle. Used to
direct the fuel in the opposite direction
you want to go.
Energy
So where can we get the energy from?
Easiest to get is from chemical energy. So
you need to have 2 substances. A fuel and
an oxidizer.
When the two substances react energy is
released.
Fuel
What “fuel” should we use?
If we use a chemical rocket we need to use
chemicals that allows for a lot of energy to be
released when they burn, but at the same time be
safe to handle.
Liquid oxygen and hydrogen is the best combo in
terms of efficiency. (Isp ~ 400 s)
Lots of energy is released as well as small molecular
mass, 18 amu, being thrown out the back end but
hard to develop due to cryogenic issues and large
tankage mass due to low density of H2.
Nozzle
We want the fuel thrown out the back. Inside
the chamber two chemicals react.
So here a series of a simple motor designs.
Why is the next one better than the
previous?
thrust
thrust
Smaller opening, higher pressure.
Using PV = nRT, means higher
temperature.
Higher temp means higher velocity of
particles.
Why not make the hole really tiny?
Rocket engine will blow up or be too heavy to
lift with the thrust produced.
thrust
Nozzle redirects the released particles
in a backward direction to increase the
forward thrust.
Why not make the nozzle even bigger?
2 reasons:
1. There is a mass penalty, a bigger nozzle can have a
detrimental over all effect.
2. If in atmosphere, Expansion issues involving the gas in
the nozzle.
As the gas expands in the nozzle, its pressure decreases. So
the gas can actually get below the atmospheric
conditions so the atmosphere can leak into the nozzle
increasing drag on the rocket.
If the bell is to small the gas can leak out of the nozzle
lowering over all thrust. So the nozzle should be
designed for the atmospheric conditions it is to be
launched in.
Nozzle design
Ideal
rocket
exhaust
Under
expanded
rocket
exhaust
Over
expanded
rocket
exhaust
Other Chemical Fuel sources?
Solid motors:
– Combines fuel and oxidizer..
– Simplest rocket engine but low ISP. Can’t be shut off
(Isp = 270 s)
Other fuels:
– Rubber/Nitrous oxide. Low ISP, “safer” do to non
cryogenic sources of fuel. (Isp = 235 s)
– Oxygen/Kerosene. Reasonable ISP, smaller tankage
mass. (Isp = 275 s)
– Hydrazine (Isp = 220 s) Nasty stuff…Benefit Long
storage
Nitrous motor test
From yesterdays press release
Other Energy sources
The one thing that you need is to some how get the
molecules of the fuel moving fast out the back of
the rocket. So moving fast means high
temperature.
Chemical rockets have a limited amount of energy
that can be released during the reaction.
So alternative is using a nuclear reactor and use the
fuel, preferably H2 due to low a.m.u. or even water
which is easier to store, as a coolant. The hot
“fuel”/Coolant is then thrown out the back.
How fast is dependent upon “reactor” design. Isp is
around 800 s
Electrostatics
A nuclear engine is restricted by the materials used
in the reactor.
Don’t want it to melt.
Another way is speed up charged particles is a
charged plate. So you ionize the particles and
send them in between a charged plate.
Use solar cells for the power to ionize the atoms and
to create the voltage for the plates.
This is an ion engine.
Limited power though. Isp = 3000 s.
Ion.swf
Ion Engine
Biggest problem is wear and tear on the electrodes.
They have been used for EXTENDED periods on the deep
space 1 mission, and currently on the DAWN mission.
Some satellites are now using ion engines for orbit
adjustments.
New engine design called VASIMR.
Variable Specific Impulse Magnetic Rocket.
VERY cool Technology. Best to use Nuclear reactor as a
source of energy for greater power/Thrust.
Can adjust the Magnetic field/Heating to change flow of
ions. So high thrust or low thrust.
Isp theoretically ranges from 3 000s to 30 000 s.
VASIMR Engine
Nothing in the way of the emitted ions. Almost no
wear and tear like other engine designs.
Notice the “nozzle” for this engine is the magnetic
field lines..VERY cool!!
ISP Curve
Images from
http://www.adastrarocket.com/
VASIMR.html
Rocket engine design
In General,
High Isp is low thrust,
Low ISP can have high
thrust.
Currently, low Isp high
thrust engines get us
into orbit. Ideally a
high ISP low thrust
move us around.
Comparison
Thrust to mass ratio
So to make the best rocket you need to look at the
economics.
A highly efficient engine may just weigh too much.
So a lower efficient engine may be better.
Example:
A typical Ion engine of thrust on 0.1 N has no chance
of lifting itself from the surface of the earth so no
point using it.
But in space it can easily be used to increase its
speed.
“Famous” Rockets
Saturn 5
1st stage
Lox/Ker
Other stages
Lox/LH
Space Shuttle
1st stage/2nd stage
Solid rocket
Lox/LH
“3rd stage”
Hydrazine..
NASTY stuff but
VERY reliable
Soyuz
All 3 stages
Lox/Ker
“Space Ship one”
One the $10 million dollar X-prize.
1st stage
N2O2/“rubber”
1st and 2nd stages
Lox/Ker
Falcon 1
Falcon 9
Dawn Spacecraft
Ion Engine
385 kg of Xenon
For many YEARS of firing
Tie Fighter
Twin Ion Engine
Enterprise
Warp Drive and Impulse Engines