Skydiving Physics.

[Will_Evo 0]

Ok so I have a question about skydiving in terms of physics. I am in a physics class and today we got into the idea of freefall. In our class we are assuming that every calculation we do is absent of air resistance, just because air resistance contains to many variables and could be a class of its own. Well today, everyone in my class, including the teacher and I agreed that a 120lb skydiver and a 210lb skydiver, in the absence of air resistance, would impact the earth at exactly the same time assuming they exited at exactly the same height and time.

Well then the subject moved into a discussion INCLUDING air resistance, and terminal velocities. The entire class and teacher all agreed together that a smaller person when compared to a bigger person would fall faster than a bigger person and without a parachute would impact the Earth first. Now this is where I got quite confused and asked mathematically how that would work, and explained that I AM a skydiver, and what they are saying goes against every physical experience I have encountered so far. The teacher said he didn't have time and left, but the class insisted to me that a smaller person would impact first.

I had no way to justify my reasoning behind the bigger person falling faster, just told them that small people in skydiving wear weights to go as fast as big people, and conversely bigger people wear baggier jumpsuits to increase drag thereby slowing them down.

Can any one mathematically prove that a heavier skydiver has a faster terminal velocity than a smaller one presenting the same surface area?

Zoo Crew

[linebckr83 3]

I can't wait to see the mathematics from someone that knows more than me, but I believe is has something to do with weight vs. surface area. For instance, my gf is about 115lbs and im a little over 200lb, not including gear. Even though I'm almost twice as heavy, I doubt I have twice the surface area as her. Which would explain why I have to dearch like a mofo while giving her "arch" signs so I can keep her in sight

"Are you coming to the party?
Oh I'm coming, but I won't be there!"
Flying Hellfish #828
Dudist #52

[strop45 0]

Basically you continue to accelerate until the drag you create balances the force your mass creates. i.e. the heavier person (with same drag) accelerates longer and goes faster. Frankly I'm not sure how/why anyone could argue the opposite. Try dropping a air filled ballon - now fill it with water which falls fastest??? Isn't this common sense. Both have the same drag, but the water filled ballon hits the ground first...

formulas are f=ma and drag = k(V*V)

stop accelerating when f=drag, more m more V

The difference between stupidity and genius is that genius has its limits." -- Albert Einstein

[kellja2001 0]

The way I think about it, is that mass is added in three-dimensions, surface area (proportional to drag) is added in two-dimensions.

Think of a cube, of mass 1 unit. Each of the sides is length 1 unit.

If you double the length of each (every) side, you have four times the surface area in any orientation prevalent to the oncoming airflow, but you have 8 times the mass (think of one corner of a rubix cube, and add the surrounding 7 squares).

Thus, in a perfect world where people are shaped like cubes, mass increases a power of two greater than surface area.

People are not shaped like cubes, nor is mass added evenly as they gain weight, but the same principle applies.

[Snowflake 0]

Doesn't bigger and smaller need to be defined better? In your example the "smaller" person would fall faster if he/she masses the same or more then the "bigger" person. The mass for the smaller person could actually be a little less than the big person, but I don't know the math. Now lets say the bigger person has a mass that's twice that of the smaller person. Then the bigger person would fall faster. You have to account for the density of the falling objects. To put it another way. A ton of bricks will fall faster than a ton of feathers. Unless you constrict the size of the feathers down to the same size as the bricks. Don't know if that helps. I'm sure someone who understands physics will come along and unmuddy the water.

[lolimfalling 0]

they could big just focusing on area and not weight when saying the smaller person falls faster.

a smaller person has less surface area so 100 pound 'small' person will fall faster than a 100 pound 'big' person because the bigger person will have more surface area to resist the wind to slow themselves down.

if by bigger they mean heavier they every1 in ur class is retarded lol, the heavier u fall with air resistance the faster u fall as uve seen on ur skydives and the exact reason why things like weight belts exist.

and ps: i didnt take the time to read everyone else's responses so sry ive im repeating something that has already been said.

[DrewEckhardt 0]

Quote

Ok so I have a question about skydiving in terms of physics. I am in a physics class and today we got into the idea of freefall. In our class we are assuming that every calculation we do is absent of air resistance, just because air resistance contains to many variables and could be a class of its own. Well today, everyone in my class, including the teacher and I agreed that a 120lb skydiver and a 210lb skydiver, in the absence of air resistance, would impact the earth at exactly the same time assuming they exited at exactly the same height and time.

Assuming people are roughly the same shape, weight is proportional to height cubed while surface area is only proportional to heigh squared. Since drag is proportional to surface area at a given speed and proportional to the square of velocity, big people must have a higher terminal velocity to produce 0 net force when drag meets their attraction to the planet due to gravity.

[billvon 2,998]

>The entire class and teacher all agreed together that a smaller
>person when compared to a bigger person would fall faster . . .

The reason that is incorrect is that weight increases by the cube of size; surface area increases by the square of size. So weight goes up faster than surface area, thus force of gravity increases faster than drag as you increase jumper size.

[cocheese 0]

Dude, you're paying for that education?

Time for a field trip to the dz.

[Will_Evo 0]

lol actually Im not I am in the Army, and am being paid to go to school, but at a very fast pace, I started physics on Monday and have my Final exam in 13 days lol. So anyone have an actual formula? I need to be able to prove what I am telling them.

-Evo

Zoo Crew

[cocheese 0]

Just tell em "the cheese burger eaters fall faster than the salad eaters."

Density = acceleration

[bfilarsky 0]

The equation for terminal velocity is Vt = ((2MG)/ρACd)^(1/2)

Vt is terminal velocity
M is Mass
G is Acceleration due to gravity (9.81 m/s^2 on earth)
ρ is density
A is area
Cd is Coefficient of drag

The only two factors that change with a change in body size, presuming the same basic shape are Mass and Area. As mentioned, mass increases more than surface area, so the fraction M/A goes up, increasing Vt.

Confused yet?

[rasmack 0]

Quote

>The entire class and teacher all agreed together that a smaller
>person when compared to a bigger person would fall faster . . .

The reason that is incorrect is that weight increases by the cube of size; surface area increases by the square of size. So weight goes up faster than surface area, thus force of gravity increases faster than drag as you increase jumper size.

+1

This is the simplest explanation to throw at anyone.

HF #682, Team Dirty Sanchez #227
“I simply hate, detest, loathe, despise, and abhor redundancy.”
- Not quite Oscar Wilde...

[mjosparky 4]

My head hurts, I am going to go lay down.

Sparky

My idea of a fair fight is clubbing baby seals

[MrDree 0]

Take a look here --> http://www.iop.org/EJ/article/0031-9120/25/5/311/pev25i5p267.pdf?request-id=07735f9a-1078-4453-8db6-8e3b2cc9482a

"One day, your life will flash before your eyes. Make sure it's worth watching."

Dudeist Skydiver #101

[Will_Evo 0]

Hmm yea, that equation is much to complicated to explain haha. I am still having a hard finding velocities and acceleration let alone drag. Oh well, I will just emphasize my physical experience, and hope it shuts them up. It was just so frustrating to hear them all agree about something that i KNOW is not true, but can't explain. Thanks for the replys.

-Evo

Zoo Crew

[muz 1]

They meant a smaller/bigger person (in size) with same weight maybe. In that case it'd be true, due to reduced air resistance of the small person.
But bigger people unfortunately, as billvon correctly put it, are quite a bit heavier :)

[Tolgak 0]

Quote

They meant a smaller/bigger person (in size) with same weight maybe. In that case it'd be true, due to reduced air resistance of the small person.
But bigger people unfortunately, as billvon correctly put it, are quite a bit heavier :)

This is exactly the point I was going to make.

Size and weight are not interchangeable. They aren't wrong, you're just interpreting their intentions wrong.

Of two people of the same weight, the one with smaller frontal surface area will go faster. Of two people of the same frontal surface area, the heavier one will go faster.

That's all there is to it.

Dropzones are terrible places for inspiration. What does one think when one looks up for a sign only to see a bunch of people falling?

[format 1]

Get your class together, hop on the table, bring a foot big cardboard box side.
Now chip off small peace and ask everybody who wants to bet a beer that small peace will hit the floor first.

Let them calculate - you go enjoy beer..s


edit: you better be current at this demo.. so practice

What goes around, comes later.

[pchapman 279]

Quote

Hmm yea, that equation is much to complicated to explain haha.
-Evo

The one block vs. 8 block explanation is still a simple way.

At terminal velocity, with speed unchanging, drag has to equal weight to balance things out. (Otherwise like in a vacuum the object would keep on accelerating.)

That one block has 1 unit of drag area per unit of weight, while the 2 by 2 by 2 set of blocks has 4 units of drag area for 8 units of weight. So that big "doubled in size" Star Trek Borg cube of eight blocks have half the drag per unit weight compared to the single block.

Which would be the same as having individual blocks that are streamlined to halve the drag.

That's why if an ant falls off a tall building, it floats away and gets lost, a mouse bounces and runs off, a cat sometimes survives injured, a human ends up with cops and yellow tape all around, and a whale splatters. Not that I've actually tested this...

Or to hit them with another equation, we know weight equals drag at equilibrium terminal velocity.

Meanwhile the basic equation for drag is:
Drag =
0.5
*
Air density
*
Velocity squared
*
Area
*
Drag Coefficient

When weight is doubled, the value of the drag equation has to double too to stay in equilibrium. Given the same shape object (same drag coefficient basically), the drag area has to double. But in our 8 block case weight is up 8 times, but area presented to the wind is up only 4 times.

So the only thing that can happen is velocity squared doubles .... the eight blocks end up falling 41% faster.
(Root 2 = 1.41, in case the class can't hack that math.)

[MakeItHappen 15]

Quote

Can any one mathematically prove that a heavier skydiver has a faster terminal velocity than a smaller one presenting the same surface area?

yes

BTW, assuming the drag coefficients are equal means that both jumpers have the same body position.
The attached graph cannot be used to compare one person in HD and one person in flat flying.

.

.
Make It Happen
Parachute History
DiveMaker

[jcd11235 0]

Quote

Hmm yea, that equation is much to complicated to explain haha. I am still having a hard finding velocities and acceleration let alone drag. Oh well, I will just emphasize my physical experience, and hope it shuts them up. It was just so frustrating to hear them all agree about something that i KNOW is not true, but can't explain. Thanks for the replys.

-Evo

It's not as complicated as it appears in text. See the attachment.

V_t (V sub t) is terminal velocity in meters per second.
m is mass in kilograms.
g is acceleration due to gravity, approximately 9.8 meters per second per second.
Rho (the greek letter that looks like an italicized lowercase p) is the air density (mass per unit of volume).
A is the projected area of the object, in meters squared
C_d (C sub d) is the drag coefficient of the object.

Math tutoring available. Only $6! per hour! First lesson: Factorials!

[wildcard451 0]

Quote

Quote

Hmm yea, that equation is much to complicated to explain haha. I am still having a hard finding velocities and acceleration let alone drag. Oh well, I will just emphasize my physical experience, and hope it shuts them up. It was just so frustrating to hear them all agree about something that i KNOW is not true, but can't explain. Thanks for the replys.

-Evo

It's not as complicated as it appears in text. See the attachment.

V_t (V sub t) is terminal velocity in meters per second.
m is mass in kilograms.
g is acceleration due to gravity, approximately 9.8 meters per second per second.
Rho (the greek letter that looks like an italicized lowercase p) is the air density (mass per unit of volume).
A is the projected area of the object, in meters squared
C_d (C sub d) is the drag coefficient of the object.

I like the MS Paint version better.

[Hellis 0]

ask your teacher to explain why a tandempilot uses a drouge.
doubble mass almost the same windresistance.
you could show him this video for example:
http://www.youtube.com/watch?v=MjIlIWSbN7E (fastforward a minute)
it clearly shows tandem/drouge and other skydivers without a drouge having the same fallrate

[jcd11235 0]

Quote

I like the MS Paint version better.

Sorry, I guess I missed the MS Paint version. In which post was it found?

Math tutoring available. Only $6! per hour! First lesson: Factorials!