Black Brant Project - Stress Analysis

Airframe Stress Analysis

Below is some documentation to try and determine the exact strength needs of the airframe. This page is based upon some guesses about thickness' and weights. It will be updated during the construction phase when we get some real numbers to plug in. A special thanks to Oliver Arend who found an error in the first go-round of calculations.

Stress Overview

	The airframe will have to withstand the compressive loading due to drag and acceleration.
	It will also have to withstand the bending stresses as the rocket corrects it's flight path.

Compressive Strength

	Compressive strength will be the strength needed to withstand not only the drag on the rocket, but also the acceleration of the airframe.
	For these calculations it was assumed the that fins would be secured to the internal structure and would not be added to the overall compressive forces.

Figure 1

Figure 2

Drag

	The plot in figure 1 shows a graph of the total drag on the airframe.
	From this graph we see that the maximum drag on the airframe occurs at approx. 3.75 seconds into the flight.
	Maximum drag appears to be about 13,500 Newtons (3,033 pounds).
	Using Rocksim it is determined that "Fin Drag" represents 45% of the total drag.
	Therefore a force of 7425 Newtons (1,668 pounds) must be acting on the the nose cone, and body tube.
	This value will be used as the maximum compressive force on the airframe due to drag. This value is in error as the forces are not distributed evenly along the airframe but will give us a good worst-case figure. Stress at any point in the airframe will be less than this value.
	A flat thrust curve is assumed for the three "P" motors giving us a force of 27,000 Newtons (6,067 pounds)

Acceleration Component

	The acceleration component represent the additional compressive loading on the airframe due to acceleration .
	From the graphs on the right, about 9.8 Gees will be the maximum acceleration.
	The G-force will be acting on all masses supported by the airframe.
	From Rocksim we get the initial (empty) mass of the rocket to be 369 pounds.
	From this we subtract the engine mount and the fins leaving us with 261 pounds of nose cone, airframe, and internally supported structures.
	By multiplying 9.8 Gees times the mass of 310 pounds we get and additional compressive loading of 2557 pounds.
	Again this is a worst-case value as the stress at any one point along the airframe will depend upon it's location.

Compressive loading total

	Drag accounts for 1,668 pounds.
	Thrust gives us and additional 6,067 pounds on the airframe.
	With acceleration placing an additional 4,650 pounds of force on the airframe.
	The total combined forces equals 12,385 pounds.
	Using a design safety factor of 1.5 the airframe must be designed to withstand 18,577 pounds of compressive force.
	Wow, that's a lot of force.