3. Parachute Design
When analysing a vehicle's flight path, it will most likely become clear that one requires a parachute for a safe landing. In engineering terms, you need to increase the vehicle's drag area (CdA) to ensure a safe landing. Assuming that propulsive deceleration is not feasible for smaller missions, you are left with either drag plates or a parachute system as a decelerator. The initial sizing for both systems is identical.
Parachute sizing
When the terminal velocity is higher than the required landing velocity, you require a parachute. The parachute drag area is determined based on the desired delta-v the parachute system has to deliver:
Here the area A is the area in m2 of the parachute, the Cd is the drag coefficient of the parachute. Finally, the delta-v is the difference between the terminal velocity calculated in section 2 and the desired landing velocity. When you do not have a parachute drag coefficient yet, you can determine the drag area (CdA) the parachute has to generate. In this way, one does not need to select the parachute type yet. For this the conceptual parachute design Excel sheet can be used.
Inflation conditions
There are two important things to consider when inflating a parachute: the Mach number and the dynamic pressure.
As a general guideline, it is not advised to deploy a parachute at supersonic or transonic conditions. When parachute inflation occurs in these regions, it is advised to change the vehicle's ballistic coefficient or the parachute deployment altitude to ensure subsonic deployment. When this is not possible a drogue parachute will be required to slow the vehicle down ensuring the main parachute is inflated at subsonic conditions.
The dynamic pressure is important as it determines the deceleration of the payload and the forces involved with parachute inflation. When these are too high it is recommended to reef the parachute or add a drogue parachute. Reefing of a parachute is the stepwise opening, limiting the initial exposed area of the parachute. When reefing is not the preferred solution it is also possible to use a drogue parachute for the same purpose. It is up to the engineers to trade-off the solutions taking into account amongst others testability, experience, mass, cost, and availability.
To get a first-order estimation of the parachute inflation loads one can use the following equation:
where:
In this equation q is the dynamic pressure in Pa, this can be obtained through simulation tools and the CdA can be obtained through previous equations. Note that this rough estimation does not take parachute inflation time and behaviour into account. The factor of 2 provides a representation of the dynamic behaviour and uncertainty in the parachute inflation. This simple rule of thumb is a good starting point for small payloads, but might not be valid for large, heavy and/or supersonic parachutes.
During the parachute inflation, the vehicle already decelerates leading to lower inflation loads when the parachute is fully deployed. For small parachutes, the inflation time can be neglected as the opening time is near-instantaneous. To determine the influence of the parachute inflation time on the decelerations one can use the Excel sheets provided on the website. These can be found here. In these sheets, you can also see the parachute's drag as a function of the total drag generated.
Canopy type and lines
There are many types of canopies available for parachute systems. The selection of the canopy depends on the dynamic pressure and Mach number at inflation, stability requirements, and general experience with a type of canopy. For small vehicles, the dynamic pressure and Mach number are low enough, any canopy type will suffice. In both cases, it is recommended to opt for a parachute canopy that the team has experience with or for which the most information is available to the team. When inflation conditions do become a problem, the team can opt to select a slotted or even a ribbon parachute. In these cases, it is always recommended to see if a change to the rocket body can mitigate the need for a different parachute type. For most parachute missions a nylon canopy is sufficient. Nylon has a very high strength to weight ratio but one has to be careful with heating, as Nylon quickly loses its strength at higher temperatures. When the temperature of the parachute becomes a problem one can look into materials such as aramids.
The lines of the parachute, both the suspension line and riser, should be sized based upon the inflation loads. As parachute inflation is a very dynamic event it is recommended to apply a safety factor of at least 1.5 and recommended is 2. Loads of parachute inflation are distributed across multiple suspension lines and these can thus be less strong. However, one should always assume the worst when it comes to asymmetric inflation. This means that a temporary high force can be exerted on one side of the parachute. It can be recommended to investigate different materials for the suspension lines as it is preferred to keep them as thin as possible. For missions to low altitude, heating on the lines should not be a problem. Only when deploying parachutes in the supersonic regime this might become an issue. In this case, it is recommended to look into thermally stable materials such as aramids.
Other considerations and requirements
One other consideration for a parachute system is clustering. This is a useful technique when the required parachute is larger than what a team can produce or test or when a "one parachute out" landing is required for a high-reliability landing. For the latter you can also consider adding a backup parachute as seen in the Soyuz capsule. Other considerations for parachute systems can be the descent time which a later deployment can mitigate.
