Multistage rocket
(Redirected from Multi-stage)
"Second stage" redirects here. For other uses, see diving regulator and reading (legislature).
"Third stage" redirects here. For the Boston album, see Third Stage.
Launch of a Black Brant 12 multistage sounding rocket
The second stage of a Minuteman III rocket
A multistage (or multi-stage) rocket is a rocket that uses two or more stages, each of which contains its own engines and propellant. A tandem or serial stage is mounted on top of another stage; a parallel stage is attached alongside another stage. The result is effectively two or more rockets stacked on top of or attached next to each other. Taken together these are sometimes called a launch vehicle. Two-stage rockets are quite common, but rockets with as many as five separate stages have been successfully launched. By jettisoning stages when they run out of propellant, the mass of the remaining rocket is decreased. This staging allows the thrust of the remaining stages to more easily accelerate the rocket to its final speed and height.
In serial or tandem staging schemes, the first stage is at the bottom and is usually the largest, the second stage and subsequent upper stages are above it, usually decreasing in size. In parallel staging schemes solid or liquid rocket boosters are used to assist with lift-off. These are sometimes referred to as 'stage 0'. In the typical case, the first-stage and booster engines fire to propel the entire rocket upwards. When the boosters run out of fuel, they are detached from the rest of the rocket (usually with some kind of small explosive charge) and fall away. The first stage then burns to completion and falls off. This leaves a smaller rocket, with the second stage on the bottom, which then fires. Known in rocketry circles as staging, this process is repeated until the final stage's motor burns to completion. In some cases with serial staging, the upper stage ignites before the separation- the interstage ring is designed with this in mind, and the thrust is used to help positively separate the two vehicles.
1 Performance
2 Component selection and sizing
3 Optimal staging and restricted staging
3.1 Optimal
3.2 Restricted
4 Tandem vs parallel staging design
5 Upper stages
6 Passivation and space debris
8 Separation events
9 Delta-v
Performance[edit]
Cutaway drawings showing three multi-stage rockets
Apollo 11 Saturn V first-stage separation
The second stage being lowered into the first stage of a Saturn V rocket
A diagram of the second stage and how it fits into the complete rocket
The main reason for multi-stage rockets and boosters is that once the fuel is exhausted, the space and structure which contained it and the motors themselves are useless and only add weight to the vehicle which slows down its future acceleration. By dropping the stages which are no longer useful to the mission, the rocket lightens itself. The thrust of future stages is able to provide more acceleration than if the earlier stage were still attached, or a single, large rocket would be capable of. When a stage drops off, the rest of the rocket is still traveling near the speed that the whole assembly reached at burn-out time. This means that it needs less total fuel to reach a given velocity and/or altitude.
A further advantage is that each stage can use a different type of rocket motor each tuned for its particular operating conditions. Thus the lower-stage motors are designed for use at atmospheric pressure, while the upper stages can use motors suited to near vacuum conditions. Lower stages tend to require more structure than upper as they need to bear their own weight plus that of the stages above them, optimizing the structure of each stage decreases the weight of the total vehicle and provides further advantage.
On the downside, staging requires the vehicle to lift motors which are not yet being used, as well as making the entire rocket more complex and harder to build. In addition, each staging event is a significant point of failure during a launch, with the possibility of separation failure, ignition failure, and stage collision. Nevertheless the savings are so great that every rocket ever used to deliver a payload into orbit has had staging of some sort.
One of the most common measures of rocket efficiency is its specific impulse, which is defined as the thrust per flow rate (per second) of propellant consumption:[1]
= When rearranging the equation such that thrust is calculated as a result of the other factors, we have:
These equations show that a higher specific impulse means a more efficient rocket engine, capable of burning for longer periods of time. In terms of staging, the initial rocket stages usually have a lower specific impulse rating, trading efficiency for superior thrust in order to quickly push the rocket into higher altitudes. Later stages of the rocket usually have a higher specific impulse rating because the vehicle is further outside the atmosphere and the exhaust gas does not need to expand against as much atmospheric pressure.
When selecting the ideal rocket engine to use as an initial stage for a launch vehicle, a useful performance metric to examine is the thrust-to-weight ratio, and is calculated by the equation
The common thrust-to-weight ratio of a launch vehicle is within the range of 1.3 to 2.0.[1] Another performance metric to keep in mind when designing each rocket stage in a mission is the burn time, which is the amount of time the rocket engine will last before it has exhausted all of its propellant. For most non-final stages, thrust and specific impulse can be assumed constant, which allows the equation for burn time to be written as
∆t = Where and are the initial and final masses of the rocket stage respectively. In conjunction with the burnout time, the burnout height and velocity are obtained using the same values, and are found by these two equations
When dealing with the problem of calculating the total burnout velocity or time for the entire rocket system, the general procedure for doing so is as follows:[1]
1. Partition the problem calculations into however many stages the rocket system comprises.
2. Calculate the initial and final mass for each individual stage.
3. Calculate the burnout velocity, and sum it with the initial velocity for each individual stage. Assuming each stage occurs immediately after the previous, the burnout velocity becomes the initial velocity for the following stage.
4. Repeat the previous two steps until the burnout time and/or velocity has been calculated for the final stage. It is important to note that the burnout time does not define the end of the rocket stage's motion, as the vehicle will still have a velocity that will allow it to coast upward for a brief amount of time until the acceleration of the planet's gravity gradually changes it to a downward direction. The velocity and altitude of the rocket after burnout can be easily modeled using the basic physics equations of motion.
When comparing one rocket with another, it is impractical to directly compare the rocket's certain trait with the same trait of another because their individual attributes are often not independent of one another. For this reason, dimensionless ratios have been designed to enable a more meaningful comparison between rockets. The first is the initial to final mass ratio, which is the ratio between the rocket stage's full initial mass and the rocket stage's final mass once all of its fuel has been consumed. The equation for this ratio is