Rich and Mike have talked about the two main issues you need to consider when rating your overall recovery system for the proper amount of stress weight load limit. Those considerations are the amount of “G” load your rocket will be subject to and the load limits of the components in your system.
First, let’s discuss the G-forces you need to consider.
Normally, the highest recovery load limit your rocket will encounter is when the main parachute deploys. To calculate this, we need to think about the “deceleration” encountered. I put deceleration in quotes because the physicists among us will balk at the use of the term since deceleration is merely acceleration vectored backwards, but, for simplicity’s sake, we will use the term here.
To calculate deceleration, we use the simple formula:
S i 2 – S f 2 / 2 x d
Where:
S i = Initial speed (fps)
S f = Final speed (fps)
d = distance (ft) required to go from Si to Sf
Once we have the deceleration, we divide by 32 (gravity’s acceleration on earth) and that will give us the G’s
Multiply that by the weight of your rocket and you then know how much “shock load” your recovery system needs to handle.
Let’s first look at a nominal flight of a rocket weighing 20 pounds.
Let’s assume the flier has chosen a drogue that will result in a descent rate of 70 fps and main that results in 20 fps. Let’s also assume the main parachute deploys quickly and achieves that speed in 50 feet. Thus, we get:
Deceleration = 702 – 202 / 2 x 50 = 4900 – 400 / 100 = 45 ft/sec/sec
G’s: 45 / 32 = 1.4 G
Load limit = 20 lbs x 1.4 = 28 lbs
So, on a nominal flight, a 20 pound rocket in this scenario would need a recovery system that could handle 28 pounds of shock loading.
Let’s look at the absolute worst case scenario, which would be the main coming out right after motor burnout (unlikely, but, for the purpose of looking at worst case, this would be the rocket’s highest velocity during flight). This worst case scenario should be calculated using the largest motor the rocket would be expected to fly on.
Let’s use 750 fps (about 500 MPH) for this calculation. That is a fairly common speed achieved by Level 2 rockets.
Let’s assume it takes a little longer for the main to slow the rocket down at this speed and use 100 feet for the stopping distance (and assume the main parachute doesn’t shred when it deploys at this speed), we get the following:
Deceleration = 7502 – 202 / 2 x 100 = 562,500 – 400 / 200 = 2810.5 ft/sec/sec
G’s: 2810.5/32 = 87.8 G
Load limit = 87.8 x 20 = 1756 lbs
It is unlikely that a main would deploy right at motor burnout, but, if you were trying to calculate the absolute worst case of a 20 pound rocket with a max velocity of 500 MPH, you would need to ensure your recovery system is capable of handling a shock load of 1756 lbs.
Once you know your worst case, you have to do some risk analysis to determine how you want to proceed. For a 20 pound rocket, it isn't very difficult to design a recovery system to handle 2000 lbs of shock loading, so you can probably do that without significant financial or technical difficulty. For a 100 pound rocket, though, you will probably need to limit your risk acceptance to something lower than absolute worst case. In our example above, a 100 pound rocket would need a recovery system capable of handling a shock load close to 9000 pounds. This is probably not realistic on a hobby budget, so you would probably want to look at "most likely worst case" scenarios, like a drogue that fails to deploy.
To address the load limits of the hardware, Mike is absolutely right – you need to be careful of what the advertised load limits for each component are. Frankly, if you buy the components on Amazon, it is a crap shoot. You often have no idea if the limits listed are working load, shock loads, etc. Further, you have no real confidence they are even telling the truth. If I buy on Amazon, I personally target a number that is about double the limit I think I need, just to be safe. If you buy from someplace like McMaster-Carr, you can be more than reasonably sure they are giving you accurate information about the hardware, but you will probably pay a premium. In my lighter rockets, I just go with the cheaper stuff on Amazon and assume the load ratings are low. For my big expensive rockets, I only use hardware I get from places like Mcmaster-Carr.
Also, don’t forget that you need to rate the load limit of the entire recovery system from the eye-bolt in the nosecone tip right down to your motor mount. If you get a bunch of swivels and quicklinks with a high load limit rating and then the non-forged eye-bolt opens up or a cheap piece of all-thread strips out or the nylon shock cord burns through, your rocket will still come burning in. Start at the nosecone tip and follow the recovery system all the way to the aft end and look for any weak points.
(side rant – I wish this forum had the capability to do subscripts and superscripts!)
(edited side rant – I wish the text formatting on this forum allowed subscript and superscript without using HTML codes!)