Analysis of Hermes Drogue Parachute

Theory and Background

A rocket with enough potential to ascend above 80,000 ft creates two difficulties for recovery. First, if the angle of attack is ideal and the motor over performs deployment dynamic pressure will be low but the payload will travel transonic under drogue. Steady state speed will be transonic, and deployment force will be small. Second, if the angle of attack is poor, then the rocket will apogee at lower altitude but with a large horizontal velocity, so dynamic pressure will be very large. Deployment speed will be transonic and deployment force will be large. This case is the most harmful one.
The extreme values in the set of apogee altitude and velocity pairs determine the limits of the drogue parameter space. Therefore, the drogue design is quantified by determining possible apogees. The Mach number vs altitude plot with constant energy (free fall velocity curves) and dynamic pressure contours (steady-state horizontal velocity curves) (right plot on figure) provides insight in to recovery dynamics. As the rocket approaches apogee, its flight curve approaches an energy contour (black lines) from above. At apogee, it crosses the contour. If apogee occurs below the drogue's state state horizontal velocity contour, max dynamic pressure occurs must be below the intersection of the two contours. If the rocket apogees above the drogue contour, then max dynamic pressure occurs at deployment. The horizontal intercept of the energy contour is the theoretical maximum altitude of the rocket. For small deviations in launch angle and wind, apogee occurs along on the same energy contour. For large deviations, the rocket spends longer in the high air density range and loses more energy to drag, so it would apogee on a lower energy contour. Running simulations with different thrust curves and drag parameters with generate a set of potential curves. The set of possible apogees is then bounded by these curves and the upper limit dynamic pressures of these simulations. The most recent ascent model of the rocket is plotted on the green line for comparison. The right chart looks at the mast ratio of the rocket and atmosphere, which is the other major predictor of deployment force.
The steady-state horizontal velocity curves are contours at constant drogue CdS. Maximum permissible drogue deployment force (which directly or slightly less than proportional to dynamic pressure (Wolf, 3rd International Planetary Probe Workshop, 2003) or maximum permissible drift set the lower limits for CdS. The maximum tolerable descent rate or permissible main deployment force, or the minimum requirements for transonic stability will put a upper limit on CdS.
From the figure it can be seen that if flight is variable to more than 10,00 ft, transonic deployment is possible, and if the rocket is capable of traveling above 100,000 ft, transonic steady-state descent is possible. Thus, a parachute with good transonic performance is required. At M > .8, non-porous hemispheric canopies flutter violently and are unreliable, so a heritage design is out of the question. This leaves the recovery team with two parachute options: conical ribbon or disk-gap-band.
Disk-gap-band parachutes where designed in the 1960s for rockets about the size of Hermes which attained comparable attitudes. The majority of modern application have been at low dynamic pressure on interplanetary probes (Viking, Huygens, MSL, etc). Although conical ribbon parachutes have a better design linage and are slightly more stable, they are considerably more difficult to manufacture. The rocket will only fly with a conical ribbon if later analysis shows that deployment dynamic pressure will be high or deployment will be chaotic.

Current Analysis

I ran 15 sims of the rocket pre-new motor at various launch angles and masses. The above figure shows conditions at apogee +/- 10 seconds. From this, one can calculate deployment forces and see that the deployment dynamic pressure will likely be less that the steady-state descent dynamic pressure.

 

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