Shape of a Rocket
Why are rockets cylindrical in shape and conical at the top?
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Every wondered why all rockets have a similar shape i.e. a near cylindrical structure with a near conical top?
Let’s understand the science behind this:
Basically, three forces affect a rocket during its flight: thrust, gravity and air resistance. While gravity and air resistance (also called drag) try to hold the rocket down, the thrust must overcome these to propel the rocket upward.
Let’s focus on the third force i.e. air resistance or drag.
Drag is the resistance or frictional force experienced by any object moving through air. It can be reduced, but not eliminated. But this requires knowledge of various factors affecting the drag. The total drag force is given by the equation:
where,
FD is drag force,
ρ is the density of the fluid,
A is the frontal area,
CD is the drag coefficient (dimensionless), and
v is the flow velocity relative to the object.
First is ρ, the density of the fluid (in our case air), which the engineers have less control over it.
Second, is the frontal area. It is the area one would see when looking directly down on a rocket as it is resting in a vertical position. As this parameter is directly proportional to drag, the lesser the area the better. From Figure 1, we get an idea about different cases. A right balance needs, to be maintained to minimize the area and also accommodate rocket’s essential components. For a given perimeter, circle provides a largest area as compared to any other shape. So engineers try to reduce the diameter of the circle by making it slender.
Figure 1: Frontal area vs Drag
Third, is the CD, the drag coefficient. This takes into account the shape of the rocket. It includes a combination of several factors: form drag, induced drag and skin friction drag.
Form drag is due to the shape of the rocket, refer Figure 2. For example, a rounded shape has less drag than a blunt shape, because the air flows over the surface easier.
Induced drag is produced by the fins and wings of a rocket. Whenever a lift force is produced, induced drag is also produced, refer Figure 3. It is a result of air flowing around the tip edge of the wing or fin from the high pressure side to the low pressure side.
(Also search about “Sears–Haack body”. It is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume.)
Skin friction drag is caused by the air particles in the airstream being slowed down by the microscopic bumps on the surface of the rocket. This type of drag can be reduced by making the surface of the rocket as slick and smooth as possible without any sharp or abrupt edges.
Other than this, other factors which favors such a design are:
- Cylinders are easy to make at large sizes.
- Pressure vessels are round, as it provides maximum strength from internal pressure (Max Q). So, a cylindrical shape ensures less weight of the rocket’s walls. (Same justification for oil tankers to be cylindrical in shape).
- Outer casing of cylinder brings in line with internal structures like fuel tanks, tubes, ducts, wiring etc. This ensures area optimization.
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