In Part 1, we talked about exhaust velocity as a measure of a rocket’s energy. That is a gross measure of what can be achieved with a given propellant. But a more comprehensive measure is one that indicates the energy obtained from a given amount of propellant—usually a pound. This measure is called Specific Impulse, or Isp. It measures how long a pound of propellant can produce a pound of thrust. Because it measures the time the pound of propellant can produce the thrust, Isp is measured in seconds.
But you can see that the more propellant burned per second, the greater the Isp, so Isp has a mass component. The amount of propellant fed to the engine per second affects its value.
This equation defines the unit:
Isp = F / (dot m * g0)
F is the force applied to the rocket by the engine
dot m is the mass rate of flow of the propellant per second
g0 is the acceleration of gravity at the Earth’s surface (in ft/s2 or m/s2)
For a rocket, which carries all its propellant on board, this can be written as
Isp = ve/g****o
ve is the average exhaust speed along the axis of the engine in (ft/s or m/s)
g0 is the acceleration of gravity at the Earth’s surface (in ft/s2 or m/s2)
Obviously, we can determine the exhaust velocity of the propellant from this equation by rewriting it
Ve = Isp g0.
All propellant combinations have differing Isp’s. Here are a few:
- liquid oxygen, kerosene (LOX/RP-1): 310
- liquid oxygen, liquid hydrogen (LOX/LH2): 455
- fluorine, hydrogen (F2/H2): 465 (not used due to extreme corrosiveness)
- nitrogen tetroxide, unsymmetricaldimethylhydrazine (N2O4/UDMH) (storable fuel): 290
- typical solid fuels: 170 – 250
- plasma jet, arc jet: 300 – 700 (very low thrust)
An ion jet can achieve an Isp of 10,000, but the thrust is in the hundredths of pounds.
Liquid Rocket Engines
The propellants we’ve talked about are used in liquid rocket engines. These powerful devices burn the fuel and oxidizer under extreme pressure and heat to produce the thrust that propels rockets into orbit, and to the planets.
But it takes more than just letting the chemicals explode in a chamber. If that’s all that happened, little thrust would be created. The gases generated by the controlled explosion must be sped up to supersonic velocity. This is accomplished utilizing what is known as the Venturi effect, named for Italian physicist Giovanni Venturi who discovered the principle in the 18th century.
This effect is such that a fluid (or gas in the case of a rocket motor) flowing from a large cylinder to a smaller cylinder increases its velocity as it flows through the smaller cylinder. Those of you who live in a city I’m sure have experienced this effect as you’ve walked between buildings and been subjected to a sudden increase in wind velocity.
The gases from the large cylinder flow through the smaller cylinder until they reach the local speed of sound. If they are then allowed to expand into another larger cylinder, they will go supersonic.
That is the basis of a rocket motor. The propellants are burned in a combustion chamber (the large cylinder), flow through a small cylinder, called the throat, and into another large cylinder called the nozzle. The nozzle is critical to the rocket engine. The gases must be allowed to expand to reach the ambient pressure of the medium they will exhaust into. Nor do rocket exhaust just expand in a linear manner. They expand in a slightly bowed shape. Thus the familiar bell shape of today’s rocket engines.
In the early days of rocketry, this was not known, and the V2 engine, for example, had a simple straight nozzle. Even the Redstone
had a straight nozzle.
Even with the bell-shaped nozzle, it is critical that the gases be expanded so their pressure matches that of the surrounding pressure while the gases remain in contact with the surface of the nozzle. If the gases reach ambient pressure before they exit the nozzle - overexpanded - they will separate from the surface. If they have not reached ambient pressure when they exit the nozzle, they will balloon out as they do - underexpanded. In either case thrust will be significantly reduced. That means a motor meant to operate mainly in the atmosphere must be shorter than one that is to operate mainly in space. The illustrations show how over and under expansion can affect the exhaust.
Over expansion causes shock diamonds to form in the exhaust because the gases are dropping below supersonic and making ‘sonic booms’ within the exhaust stream. It’s a fine sight, but reduces thrust.
Under expansion reduces thrust as well.
Engineers had a particularly thorny problem with the Shuttle’s main engines, because they had to operate from sea level to the zero ambient pressure of space. This meant the nozzle expansion had to be a compromise to get the greatest efficiency throughout the boost phase. If you’ve seen Shuttle launches from the long-range cameras, you have seen that the main engine exhaust begins to balloon out slightly as the spacecraft approaches orbit. It is underexpanded at that point.
The Rest of the Story
The heat produced by the combustion of the propellants is prodigious. It reaches as much as 6000 degrees F in Shuttle engines. No material will stand up to these temperatures, so rocket engines are cooled by circulating some of the fuel around the combustion chamber and nozzle. This is called regenerative cooling.
In the early days of high altitude sounding rockets with small motors, such as Goddard’s WAC Corporal, propellants were delivered to the motor by pressurized gas. But today’s giants burn such extraordinary amounts of propellant per second, only extremely high speed pumps can deliver the fuel and oxidizer in sufficient quantities fast enough. These pumps are driven by the same propellants burned in the engine.
There are several methods of driving the pumps. One is to use a gas generator to drive a turbine to drive the pumps, as shown in the illustration. This is acceptable for smaller engines because as can be seen some of the propellant is exhausted overboard.
Another is to use a ‘preburner’ to drive the turbine, and tap off some of the cooling liquid for fuel. The gases are then returned to the engine combustion chamber. This is a good approach for medium powered engines.
The Shuttle uses a third method. It taps the cooling liquid directly from the engine to drive the turbine, and returns it. But space scientists took this one step further for the Shuttle. Each pump has its own turbine. This is a highly efficient and reliable system.
So far we’ve talked exclusively about liquid fueled rockets. But the big strap-on boosters that get the Shuttle off the pad are solid rocket motors—the SRBs, Solid Rocket Boosters. Until Goddard flew his first liquid rocket in the ‘20s, all rockets were solids.
The SRBs are the largest, most powerful solid rockets ever made. They produce more than 3 million pounds of thrust each. The SRBs, like virtually all solid motors today, use ammonium perchlorate as an oxidizer and powdered aluminum as fuel, with iron oxide as a catalyst and a thermoplastic binder to hold it all together. The resulting mixture is called a grain.
But this mixture is not just poured into the casing in a solid hunk. A solid motor doesn’t just burn from the end. You would get a very long burn time but very little thrust that way. Rocket scientists want the entire grain to burn at once, and in a certain way, so they put a hole through the center of the grain. And not necessarily a round hole. Certain hole, or core, configurations produce specific burn characteristics, as shown in the illustration below.
The Shuttle uses an 11 point star core. But again, Shuttle, engineers threw in a twist. The star is at the forward end of the grain. At the aft end, the perforation is a double truncated cone, similar to item 5 in the illustration. This double configuration produces the high thrust needed at lift off, but then allows the thrust to drop significantly about 50 seconds into the flight when the Shuttle is going through Max Q.
Basic rocket motor: Georgia Tech https://www.ae.gatech.edu/people/ejohnson/ae1350-Fall2007/13.rockets.pdf
F1, V2, Redstone engines: Smithsonian Institution
Over expansion/underexpansion: Georgia Tech https://www.ae.gatech.edu/people/ejohnson/ae1350-Fall2007/13.rockets.pdf
Shock diamonds: NASA (personal collection)
Pump systems: Rocket and space technology https://www.braeunig.us/space/propuls.htm
Solid cores: Rocket and space technology https://www.braeunig.us/space/propuls.htm
- Personal knowledge
- Georgia Tech http://www.ae.gatech.edu/people/ejohnson/ae1350-Fall2007/13.rockets.pdf
This post is part of the series: Rocket Science–Just What is it?
Rocket science is a combination of physics and chemistry, with a smattering of aerodynamics, a bit of thermodynamics and mechanical engineering and orbital mechanics thrown in. It is a true interdisciplinary science.