The Science of Swimming Tall

It’s no secret to anyone that when it comes to swimming, length matters.  The whole notion of swimming tall and lengthening your stroke while maximizing the glide is probably not foreign to you, but few bother to think of the physics behind it.  So I offer this explanation from what I’ve learned as a design engineer of marine vessels.  I introduce you to the nerd in me:

The Math

There is a basic fundamental mathematical relation that proves that two vessels, in which all other variables are the same, the longer one will have a higher velocity.  This is a relative equation defined as the speed-to-length ratio, and it holds true for watercraft of all sizes.  For example, a canoe can have the same speed-to-length ratio as a destroyer even though their speeds and lengths are remarkably different, but because their speed-to-length ratio is proportional to these two variables it is possible for the outcome to be the same (or at least very similar).

Speed-to-length ratio = V/√L

Where V is velocity in knots, and L is vessel length in feet.

So, let’s use an example that applies to us swimmers and see how length affects speed.

Given: speed-to-length ratio = 1 (this is a typical value for a proper running hull, and one that also makes sense if the hull in question is your body)

Now, let’s take two swimmers, one 5' tall and one 6' tall, and see how they compare in the formula:

1 = V/√5, V = 2.23 knots

1 = V/√6, V = 2.44 knots

You can see clearly that as length increases so does velocity.

The Physics

So, we’ve proved mathematically that length effects speed of a vessel but what’s happening that causes that?  This is where it gets interesting.  First, let’s take the glamour out of this swimming thing and say that a swimmer – when compared to a vessel type – would best mimic a barge as it moves through the water.  I’m sorry if that hurts anybody’s feelings but, obviously, a swimmer doesn’t move fast enough to get on plane, so we can hardly call ourselves a planing vessel.  And without a sail or a deep keel the swimmer is not achieving propulsion or stability by those means.  No, the swimmer is simply pushing the water in front of it out of its way – plowing through the water – no matter how good of a swimmer you think you are.  We call this a displacement vessel, as it displaces the exact volume of water in front of it that matches its own volume in order to move forward.  In fact, it’s not just the equality of volume that is present here in the motion of the displacement vessel: the wavelength of that volume of water displaced (the wake) actually also equals the length of the waterline of the vessel itself.  As it moves through the water – as optimally as this displacement vessel can – you can see the fwd crest of the wavelength right at the bow and the aft crest of the wavelength right at the stern.  This boat moves seamlessly displacing the water as it was designed.  It’s just not all that sexy when you compare it to its planing brethren like speed boats or something you might see on Hawaii 5-0.

Now, if you could pluck this vessel out of the water and immediately put one in its place that is exactly like it in every way except it is shorter, what would you see?  The wavelength displaced by the first boat is longer than the length of the boat we just dropped in its place.  It’s like a little boat has been placed in the trough of the wake of the longer one.  Remember that the fwd crest of the first boat was exactly at the bow of that boat, and the aft crest was exactly at the stern.  This shorter boat is fitting in the trough between the two.  

The shorter vessel sits in the trough created by the longer one, with the bow wave clearly providing an uphill bulge that must be overcome.

And we know it moves slower mathematically, because we already proved that, but what’s actually happening here is the smaller boat must push uphill to gain the fwd crest of the wavelength!  And of course this causes a reduction in speed.  The water simply is not getting out of the way of the shorter boat fast enough so it therefore must be moving slower.

Or, from another perspective, if the smaller boat could maintain the speed of the larger boat it would have to increase its power monumentally over the longer boat to overcome the bulge of water at its bow.  To put it into perspective, if the taller swimmer typically swims his main set of 15 100’s at 1:10/100, and the shorter swimmer typically holds 1:17/100, imagine the increase in perceived effort it would take to overcome that speed gap.

Obviously, there are shorter swimmers that are faster than taller ones, but the physics as described above could only get us this far.  At this point, it’s up to the swimmer to overcome the physics of their inheritance and apply efficiencies to their stroke and position, the mechanics of how they apply propulsion via the kick and the catch and pull.  This is exactly why we’re taught to swim “tall,” to maximize the glide and lengthen your hull as you plow through the water in front of you.  Keep those arms in front of your head as much as you can, think about your arms existing in that “forward quadrant”, and turn yourself into the longest barge you possibly can.

You can resent the swimmer in the lane next to you that stands a foot-and-a-half taller than you with his floppy long arms, gifted as he may be in physique and stature, or you can be a good little tugboat and do the work!  It’s all in the math!