Cat Condo Build
Terminal velocity of a cat?
How long would it take a cat to hit terminal velocity and at what speed would the cat be traveling?
Weight: 13 pounds
Height: 8.7 inches
Width: 5.43 inches
Length: 11.6 inches
Thanks for your help. I'm attempting to engineer a device to deploy a parachute when an object hits terminal velocity. My condo building is 34 stories, so I am hoping it will be sufficient for this experiment.
Thanks!
I'd like to assume the cat would be spread eagle. They say cats always land on their feet, right?
The terminal velocity is found by a = 0 = g(1 - kv^2/W); where k = 1/2 rho Cd A, W = mg = 13 lbs, and rho = 1.23 kg/m^3 is std atm density, Cd ~ .5 is the cat's coefficient of drag, A = Length X Width in m^2 is the cross sectional area, and g = 9.81 m/sec^2. Then W = kv^2 and v = sqrt(k/W) = ? mps the terminal velocity you are looking for.
Remember to put everything into kms SI units (e.g., change the pounds into Newtons) before you work this.
The time to reach v is t = v/A where A is the average acceleration between v = 0 and v = v. Unfortunately, as a depends on v and v depends on a, we have a loop, which can only be solved iteratively by a computer. So coming up with the average A cannot be done manually.
You might use A = g/2 which is to assume the acceleration between zero and terminal velocity is linearly dependent on the time of fall. In which case t = v/(g/2) = 2v/g would be a rough approximation of the time to reach v, the terminal velocity. To ensure the chute deploys in time, I'd shorten my result t by a few seconds to deploy that chute with some safety margin.
By way of comparison, a human's terminal velocity reaches about 120 mph (176 fps) and, splayed out, a human's cross sectional area is way bigger than that of a cat but then so is the human's weight. The Cd's though are probably about the same. I'm guessing the terminal velocity of a cat will be about the same as that of a human.
Cat Condo Plans...Build A Cat Tree, Save Money & Your Stuff!
 |
 Kitty City Tower Scratcher CAT Condo Post Build Your Own Box Cats New Toy $28.50 Time Remaining: 28d 7h 21m Buy It Now for only: $28.50 Buy It Now |
 10 Cat Tree Plans Build DIY Furniture Condo Instruction Pattern MAKE KITTY HAPPY $9.95 Time Remaining: 24d 19h 53m Buy It Now for only: $9.95 Buy It Now |
 Plans to Build Your Own Cat Tree Cat Condo Scratching Tree More $6.95 Time Remaining: 24d 5h 26m Buy It Now for only: $6.95 Buy It Now |
