I’m a criminal who wants to make a stylish escape by parachuting off of a roof using an umbrella. Is a regular rainy-day one too small, too flimsy, or just impossible? And if so, what size should my umbrella be for success?
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Stranger
A regular umbrella is far to small and would collapse almost instantly. A typical parachute for a man is around 100 square feet in size. According to Mr. Google, the world record is 35 square feet, about the size of a bedsheet. Size-wise, you could probably get by with something about the size of a patio umbrella with an 8 foot diameter (about 50 square feet). Anything smaller and your criminal is going to make a stylish splat instead of a stylish escape.
It would also need to be a LOT stronger than a typical patio umbrella, or again, splat.
Some searching suggests that parkour athletes can handle a 6-meter drop onto flat ground (with a roll at the end). That’s 11 m/s.
Assuming that an umbrella has a Cd of 1.0, and our criminal is a relatively slim 60 kg, that gives a required area of 8.1 m^2. That’s a radius of 1.6 m, or a diameter of 3.2 m, or 10.5 feet.
So as engineer_comp_geek said, somewhere around a patio umbrella should be survivable. I’m not sure if it needs to be reinforced–after all, they aren’t usually destroyed in 25 mph winds. Not that I’d want to grab any old off-the-shelf one, though.
It gets easier if you land in sand or water, of course.
So basically grab the roof-top patio umbrella and aim for the swimming pool 10 stories down.
I guess the next question is steering. Check the wind first. IIRC movies of the old canopy parachutes like WWII paratroopers that (a) not very steerable and (b) if you start to swing, air spills out the high side causing interesting dynamics. At least with the regular canopy chutes it seems you could pull on some of the ropes to direct the spill.
Be careful how you land, don’t spear yourself in the gut with the umbrella shaft.
That would definitely be a worry. I think that jumping off a not-too-high roof would take too little time for undamped oscillations to build up too much, and you’d probably be all right (again assuming you can take a hard landing). But jumping out of a plane seems like it would be disastrous, even assuming you could hold onto the pole for that long.
Never mind boring science 
- the chap you want is the Penguin!
If you’re willing to trade some style point for a large improvement in survivability, you’d do well to study the equipment used by BASE jumpers, who regularly jump off buildings - and often survive.
They have worked on the issues of rapid & clean deployment, and how to avoid hitting the building under canopy.
They call it balconing in Spain and there are many videos in YouTube that show that it is a very bad idea that mixes horribly with alcohol and recreational drugs.
I suggest a better parachute instead of aiming for the pool.