Hello I wonder if anyone here might be able to help me. I am writing a children's book called The Wing Giver about a boy who wants to fly and a Spitfire pilot. However words are my thing and physics isn't! In the book, the boy wants to solve a formula his dad has set him which is to work out the size of parachute he would need for himself - a 70kg male. Somewhere during my research I found this formula (v(t) = sqrt(2*m*g/(p*A*(d) ) but I can't remember where from or what it is calculating exactly! Does anyone have any suggestions for a good parachute formula that would stump a ten year old boy but one that he might have the possibility of working out over time. Any ideas will be so gratefully appreciated and if I ever get published, I'll give you a thanks!!! Emma
Hi and welcome. This is a hard one. I could not find a lot of accessible stuff (old papers from Cranfield with formulae up to here) or practical parachuting articles. You need to google terms like terminal velocity, parachute and skydiving. Unfortunately, most skydiving links seem more interested in telling you how fast you'll be falling before you are using the parachute! There are several Images of graphs, showing speeds. I think most of the early development was done experimentally and the Maths is pretty hard. As you need to be using the right terms in order to be credible, you will need to read around, in any case. The two links, below, could help there and with a ballpark answer for your boy's design. That formula of yours looks like the formula for terminal velocity of a falling object (sphere?). It would be better than nothing and you could work with a velocity of say 8m/s, which is fairly safe for landing. This link has a formula for terminal velocity. This link has a value for the drag coefficient for various shapes in air. Choose the cylinder, perhaps (=1.2) Enjoy and feel free to come back.
Thank you so much Sophie and sorry for delay. Been away from computer for a couple of days Yep - don't think I've set myself the easiest challenge as it needs to be something I can write which is fairly accessible and doesn't lose readers! The parachute is quite a nice metaphor as his flying obsession is linked to grief of having lost his father but it might just be too hard... I'll look at your links now and try to work it out otherwise back to the drawing board. Thanks so much for your help. It's hugely appreciated. Emma
This link below from NASA has a small sketch (a Free Body Diagram showing all the forces acting on the parachute) and the equation for terminal velocity in the form you mentioned, where W=mg = 70*9.8 in your case: http://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/airplane/rktvrecv.html They also mention that the drag coefficient for a parachute is around Cd=1.75, which is obtained from experiments. Basically you calculate the desired drag coefficient based on the desired terminal velocity, and then design a parachute that has this drag coefficient.
Has the sums to size the parachute for a model rocket.. http://my.execpc.com/~culp/rockets/descent.html
Just embarking on my final redraft of final edit of book so all your links here are very useful and apologies for not saying thanks earlier. Just working through them now! Thank you for all your help.