# Terminal velocity under the 'chute

The descent rate given in the POH under the 'chute is for max gross weight. Does anyone know how terminal velocity will vary with mass? Single pilot with partial fuel produces an SR22 gross weight of 2800lbs or so, or only 82% of max gross. I wonder if that results in a significantly slower descent.

-Curt

Since air resistance varies with the square (or is it the cube?) of airspeed, I would expect that a reduction in aircraft weight would not produce a proportional reduction in descent rate.

Post deleted by mbnagy

My physics text says that the air resistance is approximately proportional to the
velocity.

Only for small objects at low speeds (where the resistance is primarily simple friction). With a large object at a high speed the actual relationship is complicated, but is usually approximated with a square order expression.

Here’s a bit more about fluid drag:

[]Fluid resistance is proportional to the speed v only at very low speeds where the dominant source of resistance is viscosity (the internal friction of fluids)[]At the speeds of ordinary objects in air (including bicyclists, tossed baseballs, airplanes in flight, and Cirri descending under parachutes), the force of fluid resistance is approximately proportional to v2, the square of the speed.[/list]When a Cirrus of weight W is descending under its parachute at a steady speed v, the downward force of gravity is exactly balanced by the upward force of fluid resistance. Using the v2 formula, this says that

W = kv2,
where k is a coefficient that depends on the shape and size of the parachute and the density of the air. Solving this expression for the descent speed v, we find

v = (W/k)1/2.
In other words, the descent speed is proportional to the square root (also known as the 1/2 power) of the weight W. As a rule of thumb, this means that every 2% decrease in the weight gives a 1% reduction in the descent speed.
This analysis also applies to those situations in which a person descends under a parachute without an airplane attached (amazingly, it does happen!).

Cheers,
Roger

In other words, the descent speed is proportional to the square root (also known as the 1/2 power) of the weight W. As a rule of thumb, this means that every 1% decrease in the weight gives a 2% reduction in the descent speed

Roger, do you want to rethink that slightly? I think you meant to say that a 2% reduction in weight reduces the descent speed by about 1%.

Or as a concrete example, an SR20 at 2500 lbs would descend under parachute at about 91% of the speed of the same SR20 at 3000 lbs. IOW a 17% reduction in weight reduces the descent speed by about 9% (sqrt(.8333) == .91285)

an SR20 at 2500 lbs would descend under parachute at about 91% of the speed of the same SR20 at 3000 lbs. IOW a 17% reduction in weight reduces the descent speed by about 9% (sqrt(.8333) == .91285)

Now the energy to be dissapated in the landing is mV^2. Since V~=sqrt(m), then energy is proportional to m(sqrt(m))^2 or m^2. So a 10% reduction in weight would produce a 19% reduction in energy (.9^2=.81), and my 20% reduction case in the SR22 would produce a 36% (.8^2=.64) reduction in energy. Perhaps that is why the downed SR22 didn’t look so badly damaged.

-Curt

Clyde,

Quite so! I edited my post to include the correct statement. Thanks for catching that.

Cheers,
Roger

Perhaps that is why the downed SR22 didn’t look so badly damaged.

Possibly. Another factor is certainly the shrubs it landed on.

The main gear on the downed airplane is perfect, and may not even have contacted the ground. The right wing has some damage near the wingtip, probably because it DID hit the ground. Same for the nosegear (broken off), and one blade of the prop, which was bent when the nose struck the ground. Overall, the airplane is in remarkably good condition, and I would not be at all surprised if this airplane flies again.

Mike.

“I would not be at all surprised if this airplane flies again.”

Mike,

This incident gives a new meaning to the old saying, “any landing you can walk away from, and the plane is reusable (albeit, in this case, a “little patching up” required) is a good landing” Says a lot for the chute system (and some handy shrubs).

``````On the other hand, if this plane goes up for sale in the futureÂ…"any damage history?"
``````

Walt

I’d take bets that the Smithsonian may want this airplane - since it was the first certified aircraft saved by a chute.

Actually Walt, any landing you can walk or swim away from is a good landing. Any good landing after which you can reuse the airplane without major repairs is a great landing.

As a physician for whom the word “terminal” has a different meaning I suggest we refer to this subject as “final velocity prior to impact”

Jerrold,

``````  You're right. I sit corrected!
``````

Take care,

Walt

…any landing you can walk or swim away from is a good landing. Any good landing after which you can reuse the airplane without major repairs is a great landing.
…and, as a naval aviator once told me, any landing that ends on a runway is a precision landing.

Cheers,
Roger

Jerry:

Well, then how about “final velocity before vertical landing”?

Tim

I suggest “vertical approach speed on final”

As a physician for whom the word “terminal” has a different meaning I suggest we refer to this subject as “final velocity prior to impact”

Hi Jerry,

Alas, this term has such a long history of usage that I suspect you’ll have a hard time getting too many people to change. Besides, there are plenty of scientific/technical terms that have different meanings in different fields. (An extreme example is “unionized,” which means something very different to a labor organizer than it does to a chemist.)

Then again, maybe I’m just touchy after the medical report that described my internal organs as “grossly unremarkable.” Talk about faint praise!

Cheers,
Roger

That’s perfect!!