Hi Roy... And anyone else keeping tabs on this thread
This time a very long, two part, reply
OK, Vt calculations. Terminal Velocity is:
Vt = sqrt ( (2 * m * g) / (Cd * r * A) )
Vt = sqrt ( (2 x mass_of_object x gravitic_acceleration) / (drag_coefficient x fluid_density x area of drag) )
At first I simply played with the formulas in a spreadsheet - very handy way of poking around with physics equations. And the initial results certainly supported the importance of mass that Roy was talking about.
Then I got a bit more serious about things and made sure the appropriate constants were correct (which was pretty easy). Now I did some interesting what-if analysis based on some real board dimensions, basing mass on real world reports of weight for composite, PU and HWS/solid wood boards where possible. Where real weights couldn't be found I calculated a weight based on the differences between boards of those type at smaller sizes (inexact, but probably close enough at this stage). Note that this initial batch of investigation focuses on pure Vt, without anything else being factored in. So that represents a board dropping through the air bottom down. Like an air drop down the face of a two meter wave, for example. I set the drag coefficient to a standard of 0.2, which probably isn't too far off for a surfboard (don't know for sure).
Since this is a longboarding forum I'll report on the "standard" longboards first. Results:
- 5kg 9'0" compsand. Vt = 16.1 m/s (4.7 km/h).
- 9kg 9'6" PU . Vt = 21.1 m/s (5.8 km/h).
- 20.3kg 9'3" wooden board (Roy's). Vt = 32.0 m/s (8.9 km/h).
Now, that speed is the terminal velocity of that object falling through the air bottom down in meters per second. So the difference does seem quite marked.
Now the wooden board has a Vt twice that of the compsand board... But is more than four times heavier.
But there is something else important we need to consider, too. These objects will ACCELERATE (i.e., speed up) by 9.8 meters (less the effect of drag) every second until they reach their Vt. So over a drop of two meters (or five meters) the difference wouldn't be huge. Probably measurable without too much difficulty, but not as different as the numbers above suggest.
Now what if we put an 80kg rider on the board (i.e., add 80kg to the mass)?
- 85kg 9'0" compsand. Vt = 66.7 m/s (18.5 km/h).
- 99kg 9'6" PU . Vt = 66.35 m/s (18.4 km/h).
- 100.3kg 9'3" wooden board (Roy's). Vt = 71.3 m/s (19.8 km/h).
Woah! Look at that gap in Vt drop! And with the ACCELERATION caveat I discussed above the difference will be even less noticeable.
Also interesting is that the effect of drag on an object "falling through water" due to water's higher density is more pronounced (so the impact of drag area is greater), since water is about 1,000 times denser than air.
The drag equations themselves start out very simple. And become increasingly complex. Drag is fascinating.
This is by no means
the end of the story!
With a smaller board carrying the same rider Vt almost reverses!
- 2.2kg 6'2" compsand RIDERLESS. Vt = 14.2 m/s (3.9 km/h).
- 2.7kg 6'2" PU RIDERLESS. Vt = 15.7 m/s (4.3 km/h).
- 5.8kg 6'2" HWS RIDERLESS. Vt = 18.9 m/s (5.2 km/h).
No surprises so far... Now add the rider:
- 82.2kg 6'2" compsand. Vt = 87.0 m/s (24.1 km/h).
- 87.2kg 6'2" PU. Vt = 87.2 m/s (24.4 km/h).
- 85.8kg 6'2" HWS. Vt = 73.0 m/s (20.2 km/h).
What the?! Don't be alarmed. The HWS board is WIDER. So it has a larger "A" value. Making that the same results in 88.9 m/s (24.6 km/h) for that board
Told you I used real dimensions where I could.
So that deals with the drop for speed/power generation. Less steep waves will have less of an "air drop" factor, meaning more contact with water. More of the board in contact with water will further negate the effect of mass on acceleration (I can go into this too if people are interested).
Oh yeah. I did these calculations for boards in the 6', 9', 11.5' and 17' ranges. Figures available on request.
Next I moved on to where I think mass really matters... Momentum!
Follow-up post coming shortly.