A.5.2.7 Bulkheads1
In our first attempt at designing a launch vehicle, we decide that our vehicle will have an outer skin and that the fuel tanks will be sandwiched into the external structure. We use disk-shaped bulkheadsto separate the nozzle of the upper stage from the fuel tank of the lower stage. The disk-shaped bulkhead has a hole in the center to pass electrical wires through to the stages below.
The structural analysis of the disk-shaped bulkhead results in a minimum thickness of the bulkhead to overcome the axial loading. First, we impose a deflection constraint on the bulkhead when the load is applied. The nominal thickness is calculated by solving the deflection equation for thickness. After the nominal thickness is determined, we calculate the maximum applied stress on the bulkhead, multiply the stress by the reserve factor, and compare this value to the yield stress of the bulkhead material. If the applied stress multiplied by the reserve factor is less than the yield stress, the thickness is incremented, and when the applied stress multiplied by the reserve factor is greater than the yield stress, the minimum required thickness has been found. Then, this process is repeated for each material candidate and the cost of the bulkhead is output. These costs are then compared to find the lowest cost option.
In our initial design of the launch vehicle, two bulkhead configurations were considered. The bulkhead themselves retain the same geometrical specifications for each configuration, but are attached to the outer skin differently. The first bulkhead configuration is rigidly attached to the outer skin, and the second bulkhead configuration is fixed on top of the tank below. Since the first configuration is attached to the outer skin of the launch vehicle, the bulkhead will cause more shear force to occur on that point of the launch vehicle skin, whereas the second configuration does not impact the overall vehicle. This application of force on the overall vehicle must be taken into consideration when we choose the final configuration.
First, we consider the structural analysis of the first bulkhead configuration. Figure 1 displays this bulkhead configuration in the rocket, and Fig. 2 gives the free body diagram.
Fig. A.5.2.7.1:First bulkhead configuration and upper stage
(Jesii Doyle)
Fig. A.5.2.7.2: First bulkhead configuration free body diagram
(Jesii Doyle)
First, the applied load to the cross-section must be determined. The applied load to the bulkhead is described in Eq. (A.5.2.7.1) below.
/ (A.5.2.7.1)where m is the total mass of the stages above the bulkhead, Gmax is the maximum G-loading, g is the gravitational velocity, P is the applied force, rnozzle is the radius of the nozzle in contact with the bulkhead, and w is the force per unit of circumference.1
The maximum displacement equation is shown in Eq. (A.5.2.7.2) below, solving for thickness.
/ (A.5.2.7.2)where t is the nominal thickness of the bulkhead, w is the force per unit of circumference, a is the bulkhead outer radius, b is the bulkhead inner radius, ymax is the maximum vertical displacement of the bulkhead’s free edge, υ is Poisson’s ratio, E is the modulus of elasticity, and rnozzle is the radius of the nozzle in contact with the bulkhead.1
The calculated thickness is then input into the applied stress equation, which is shown in Eq. (A.5.2.7.3) below.
/ (A.5.2.7.3)where σ is the applied stress, rnozzle is the radius of the nozzle in contact with the bulkhead, w is the applied force per unit of circumference, a is the bulkhead outer radius, t is the thickness, and R.F. is the reserve factor.1
Once the minimum thickness is found for one type of bulkhead material, the process is repeated for each possible material option. Finally, the weight and cost of each bulkhead is calculated.
Next, we consider the structural analysis of the second bulkhead configuration. Figure 3 displays this bulkhead configuration in the rocket, and Fig. 4 gives the free body diagram.
Fig. A.5.2.7.3: Second bulkhead configuration, lower stage, and upper stage nozzle
(Jesii Doyle)
Fig. A.5.2.7.4: Second bulkhead configuration free body diagram
(Jesii Doyle)
First, the applied load to the cross-section of the second bulkhead configuration must be determined. The applied load to the bulkhead is described in Eq. (A.5.2.7.4) below.
/ (A.5.2.7.4)where m is the total mass of the stages above the bulkhead, Gmax is the maximum G-loading, g is the gravitational velocity, P is the applied force, rnozzle is the radius of the nozzle in contact with the bulkhead, and w is the force per unit of circumference.1
The maximum displacement equation is shown in Eq. (A.5.2.7.5) below, solving for thickness.
/ (A.5.2.7.5)where t is the nominal thickness of the bulkhead, w is the force per unit of circumference, a is the bulkhead outer radius, b is the bulkhead inner radius, ymax is the maximum vertical displacement of the bulkhead’s free edge, υ is Poisson’s ratio, E is the modulus of elasticity, and rnozzle is the radius of the nozzle in contact with the bulkhead.1
The calculated thickness is then input into the applied stress equation, which is shown in Eq. (A.5.2.7.6) below.
/ (A.5.2.7.6)where σ is the applied stress, rnozzle is the radius of the nozzle in contact with the bulkhead, w is the applied force per unit of circumference, a is the bulkhead outer radius, t is the thickness, and R.F. is the reserve factor.1
Once the minimum thickness is found for one type of bulkhead material, the process is repeated for each possible material option. Finally, the weight and cost of each bulkhead is calculated for each material option.
Subsequently, we decided to revise our launch vehicle configuration. The new launch vehicle configuration does not have an overall external skin. Therefore, the inter-stage configuration needs to be reconsidered. This new launch vehicle design results in the use of inter-stage skirts between stages, and renders both bulkhead configurations obsolete.
References
1 Young, W.C., and Budynas, R.G., Roark’s Formulas for Stress and Strain (7th Edition), McGraw-Hill, 2002.
Author: Jesii Doyle