Old Jul 23, 2013 | 10:39 AM
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maxcichon
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From: MOFN, AL, 70 miles from George
Default Re: Need Help_ Crossfire Non-srt Top Speed Proof?

Originally Posted by ala_xfire
Mine can do that.
( dropped out of a C130 at 20,000 feet )
No way!:

Speed of a Skydiver (Terminal Velocity)

And:

In principle one doesn't know beforehand whether to apply the creeping flow solution, or what coefficient of drag to use, because the coefficient depends on the speed. What one can do in this situation is to calculate the product of the coefficient of drag and the square of the [[Reynolds number]]:
:<math>C_d \mathrm{Re}^2 = \frac{mgD^2}{A\rho\nu^2}</math>

where ν is the [[kinematic viscosity]], equal to μ/ρ. This product is a function of Reynolds number, and one can consult a graph of C<sub>d</sub> versus Re to find where along the curve the product attains the correct value (a qualitative example of such a graph for spheres is found at this NASA site: [http://www.grc.nasa.gov/WWW/k-12/air...agsphere.html]) From this one knows the coefficient of drag and one can then use the formula given higher up to find the terminal velocity.

For a spherical object, the above-mentioned product can be simplified:
:<math>C_d \mathrm{Re}^2 = \frac{4mg}{\pi\rho\nu^2}</math>

We can see from this that the regime and the drag coefficient depend only on the sphere's weight and the fluid properties. There are three regimes: creeping flow, intermediate-Reynolds number Newton's Law (almost constant drag coefficient), and a high-Reynolds number regime.<ref>''Chemical Engineer's Handbook'', edited by [[Robert H. Perry]] and [[Cecil Chilton]], fifth edition, ISBN 978-0070494787, pp. 5-61 and 6-62.</ref> In the latter regime the boundary layer is everywhere turbulent (see [[Golf ball#Aerodynamics]]). These regimes are given in the following table. The weight range for each regime is given for water and air at 1 [[atm (unit)|atm]] pressure and 25&nbsp;°C. Note though that the weight (given in terms of mass in [[standard gravity]]) is the weight in the fluid, which is less than the mass times the local gravity because of buoyancy.

{| class="wikitable"
|-
! Regime
! Range of Reynolds number
! Range of C<sub>d</sub>Re<sup>2</sup>
! Range of weight in water
! Range of weight in air
|-
| Creeping flow
| Quite accurate up to 0.3
| Up to 7.2
| Up to {{convert|0.00058|mg-f|nN|abbr=on}}
| Up to {{convert|0.00017|mg-f|nN|abbr=on}}
|-
| C<sub>d</sub> between 0.4 and 0.5
| {{gaps|1|000}} to {{gaps|200|000}}
| {{gaps|500|000}} to 2{{e|10}}
| {{convert|40|mg-f|mN|abbr=on}} to {{convert|1.6|kg-f|N|abbr=on}}
| {{convert|11|mg-f|mN|abbr=on}} to {{convert|470|g-f|N|abbr=on}}
|-
| C<sub>d</sub> between 0.1 and 0.2
| Over {{gaps|400|000}}
| Over 1.6{{e|10}}
| Over {{convert|1.3|kg-f|N|abbr=on}}
| Over {{convert|375|g-f|N|abbr=on}}
|}
Between the first two regimes there is a smooth transition. But notice that there is overlap between the ranges of C<sub>d</sub>Re<sup>2</sup> for the last two regimes. Spheres in this weight range have two stable terminal velocities. A rough surface, such as of a dimpled [[golf ball]], allows transition to the lower drag coefficient at a lower Reynolds number.
 
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