I was asked on the SDK thread about my past posts on speed and height.Here is a more complete explanation.There are 2 main forms of drag affecting swimmers:form drag and wave drag.Wave drag only occurs at the surface so it is not a factor when swimming underwater.Lack of wave drag is why SDK can be so fast even though it is less propulsive than full stroke.
Form drag is from how much water you push in front of you and pull behind you. Improved streamlining decreases form drag.There are many things we can do to decrease form drag:good body position,shaving down,technical suits,losing weight,etc.For a given shape form drag resistance increases as the square of the velocity.
Wave drag comes primarily from pushing your bow wave. There is very little drag from this until you exceed your "hull speed" at which point you are climbing up on your bow wave.At this point resistance goes up as the cube of velocity so it rapidly becomes the primary resistance.
The formula for hull speed is:hull speed(in knots)=1.34times the square root of the length at the waterline(in feet)(for a swimmer that is the height)This is why longer boats(and taller swimmers) are faster.
For example I'm 5'8" (or 5.67 ft) so my hull speed is 3.19 Kt.A knot is 1 nautical mile per hr or about 1.67 fps so my hull speed is 5.32 fps.This is doing 50 yd in 28.19 sec.Going faster than that requires disproportionally more power than going slower than that(at the surface).
What can you do to decrease wave drag?You can be tall(or at least swim tall),you can stay underwater,or you can swim slower.Obviously swimming slower is no help in a sprint,but it does mean that even pacing will use less energy than going fast for part of the race.
Here is a table I calculated of height and hull speed
Height Hull Speed(feet per sec) Time for 50 yd
5' 5 fps 30 sec.
5'3" 5.12 fps :29.29
5'6" 5.24 fps :28.62
5'9" 5.36 fps :27.98
6' 5.47 fps :27.42
6'3" 5.59 fps :26.83
6'6" 5.71 fps :26.26
And when your beer is moved from its gimballed cupholder to the skipper's digestive system, you care less, one way or the other, about how fast your hull is moving.
You are right that hull speed calculations are not exact for the human form.Really the main points are that being tall is an advantage on the surface but not underwater.Also that resistance increases rapidly above hull speed,but it is,of course possible to go faster.
If I were to somehow attach myself in parallel with a fellow swimmer, say, Amanda Beard, and in so doing create a kind of human catamaran, would the two of us go faster than the fastest of us (her) could go alone? This is assuming no odd rudder effects being generated by catamaranization.
I was assuming Amanda and I were swimming freestyle, not backstroke. To be honest, I think both "rudder" and "mast" overstate things considerably in my particular case. "Slightly enlarged dermal denticle" might be more accurate, though I suppose Amanda, given her Olympic greatness, might inspire more.
Sorry. Did not mean to steer this in non-swimming related directions.
Back post haste to form drag!
Really the main points are that being tall is an advantage on the surface but not underwater.
I'm not sure I buy this. When there is no free surface involved, such as swimming underwater, you can use classical aerodynamics more readily. A long, thin airfoil (wing) will produce less drag than a short, fat airfoil. I think a tall person has an advantage both on top of and under the water.
The hull speed formula applies to displacement-type vessels like a keeled sailboat, which can only exceed that speed when hydroplaning. A catamaran, which has two planing hulls, can beat a keeled sailboat with a much longer waterline length, as Dennis Conner convincingly demonstrated when he defeated New Zealand in the 1988 America's Cup.
Perhaps a swimmer is better characterized as "semi-displacement" or "semi-planing."
I don't know a lot of the science behind hullspeed, but I do sail and am familiar with the concept. The hull speed formula cited is an empirical approximation that apparantly works for the typical configuration of displacement hulled boats. The exact geometry of the hull certainly matters, so the application of this concept to particular hulls and extending it to the human body would be less exact.
My understanding of hull speed is that the additional power required to go faster is some sort of exponential curve which "jumps" or becomes much steeper at hull speed. Its not that you cannot go faster than hull speed (planing hulled boats do it), but it takes a lot more power to do so. The marginal return on effort becomes less.
Sailing home in rough seas yesterday, and watching my GPS, I noticed a few things that can be learned from sailing and applied to swimming:
- Splashing is a waste of energy
- You move fastest when your center of gravity is moving in a straight line (i.e. not bobbing up and down)
- You move fastest when your propulsive force is not varying and you maintain momentum.
- Always put your beer in a gimballed cupholder
Steve
Kirk,I'm not sure about the effect of length on underwater drag.In your example the key words may be fat and thin,not long and short.It would seem to me that with 2 swimmers of equal girth,the shorter swimmer would have less form drag by virtue of lees surface area,but I'm not sure.
The "swim tall" question has been vexing me.It seems to me that if your arm extension forward is disrupting your bow wave it is making your "length at the waterline" longer and hence increasing your hull speed.
Not to mention that the formulas undoubtedly were put together for steady state situations, not ones where the bow wave is dirsupted about twice per second. I suppose it remains to be demonstrated whether there is anything we can do with our entries to change the amount of wave drag we encounter. Maybe the folks doing computational fluid dynamics will look at this one of these days.
