By default, the program Input Variable is the Mach number of the flow. Since the area ratio depends only on the Mach number and ratio of specific heats, the program can calculate the value of the area ratio and display the results on the right side of the output variables. You can also have the program solve for the Mach number that produces a desired value of area ratio. Using the choice button labeled Input Variable , select "Area Ratio - A/A*". Next to the selection, you then type in a value for A/A*. When you hit the red COMPUTE button, the output values change. The area ratio is double valued; for the same area ratio, there is a subsonic and a supersonic solution. The choice button at the right top selects the solution that is presented.
If you are an experienced user of this calculator, you can use a sleek version of the program which loads faster on your computer and does not include these instructions. You can also download your own copy of the program to run off-line by clicking on this button:
We can determine the exit pressure pe and exit temperature Te from the isentropic relations at the nozzle exit:
pe / pt = [1 + Me^2 * (gam-1)/2]^-[gam/(gam-1)]
Te / Tt = [1 + Me^2 * (gam-1)/2]^-1
Knowing Te we can use the equation for the speed of sound and the definition of the Mach number to calculate the exit velocity Ve:
Ve = Me * sqrt (gam * R * Te)
We now have all the information necessary to determine the thrust of a rocket. The exit pressure is only equal to free stream pressure at some design condition. We must, therefore, use the longer version of the generalized thrust equation to describe the thrust of the system. If the free stream pressure is given by p0, the rocket thrust equation is given by:
F = m dot * Ve + (pe - p0) * Ae
You can explore the design and operation of a rocket nozzle with our interactive nozzle simulator program which runs on your browser.
The thrust equation shown above works for both liquid rocket and solid rocket engines. There is also an efficiency parameter called the specific impulse which works for both types of rockets and greatly simplifies the performance analysis for rockets.