Should You Throw Your Water Bottle When Racing a Road Bike?

The other day, with 1.5 laps left in a cat 3 crit, the guy in front of me reached down into his bottle cage, grabbed his bottle, and threw it wildly onto the sidewalk, almost hitting a spectator.

This process caused him to open up a two or three bike length gap in front of him which he then had to pedal hard to close... almost certainly negating any gains he made by losing the weight of the bottle for the final sprint.

So I'm pretty confident that this particular bottle-throwing instance was a poor decision, but it motivated me to look into the
actual savings of the bottle-throw, which is really just an excuse to blog about PHYSICS!!  And who doesn't love MATH?!

IMPORTANT NOTE:  Throwing your bottle creates trash.  Trash creates unhappy residents on race courses.  Unhappy residents create problems for race promoters.  If you're throwing your bottle onto someone's lawn -- you are the kind of racer that all promoters hate.  Don't do it.

Let's set some ground rules:

1) A full bottle weighs one pound (0.45kg)
2) The aerodynamics of your bike are basically the same with or without the bottle.
3) The placebo effect of throwing the bottle doesn't make you go faster.

We're going to use energy equations to solve this.  The equation for kinetic energy is 0.5*mass*velocity squared.

The equation for potential energy is mass*height*gravity (9.8m/s/s).

At any given moment, the energy of a water bottle is based on how fast it's moving (kinetic energy) and how high above the lowest point of reference it is (potential energy).  If the energy of the bottle changes, that energy came from YOUR LEGS.

If the sprint is uphill, what benefit does throwing the bottle give me?

The GMSR crit (scene of the original bottle throw) has one of the more uphill sprint finishes out there.  On the last lap, I came through the final turn at 38mph (17m/s).  I crossed the line 12 seconds later at 32 mph (14.3 m/s) and about 20 feet (7m) higher than the final turn.  There was a (full) water bottle on my bike -- let's look at the energy involved.

At the turn, the bottle's kinetic energy was 65.025 joules  (0.5*0.45*17*17).  It's potential energy was zero, since it's at the lowest point in its path.

My body and my bike also have significant kinetic energy here, but they have the same energy whether there's a bottle attached or not, so it doesn't matter.

At the finish, the bottle's kinetic energy was down to 46.025 joules  (0.5*0.45*14.3*14.3) because I can't sprint at 38 miles per hour up hill.  But, the bottle's potential energy was now 30.87 joules, because it had moved 7 meters higher up the hill.  Adding these together, the energy the bottle had at the end of the sprint was 77 joules, a gain of 12 joules!  

These joules had to come from somewhere (my legs), so dragging that stupid bottle all the way through the 12-second sprint cost me 1 watt on average!  

(A watt is a joule per second, so 12 seconds at 1 watt = 12 joules)

(Probably don't need to throw your bottle in this sprint since it saves you literally one watt of sprinting power)

Even if I was making so much power that I didn't slow down at all in the uphill sprint (costing me kinetic energy), the savings would have only been 2.6w. 

If the sprint is flat, what benefit does throwing the bottle give me?

Most sprints aren't uphill.  What if you're sprinting in a normal, flat crit?  You're gonna accelerate during the sprint and if you didn't have to accelerate that big fat bottle you'd, like, totally win.

Let's assume you go through the last corner at 35mph (let's face it, you're a cat 3, if you get a 35 mph leadout it's a miracle) and hit the line at 40mph (because you're awesome).  The course is flat, so the potential energy of the bottle on your bike is unchanged.  The only question is how much kinetic energy has to be added to the system to accelerate a bottle from 35mph to 40mph?

35mph energy:  55.08 J

40 mph energy: 71.2 J

Difference:  16.2 J, or 1.3 watts over 12 seconds.

(Probably don't need to throw your bottle here, either)

(Oh and there's probably no way you can accelerate from 35mph to 40 in 12 seconds, because you're a scrub, I was just using some really optimistic numbers to illustrate that throwing you bottle is basically meaningless here, too)

What if I'm at the bottom the steep part of Middlebury Gap with a full bottle on my back in the Cat 3 race?

OH LOOK ANOTHER REAL LIFE EXAMPLE!

I started GMSR Stage 3 with an extra bottle because I was worried about survival.  This bottle ended up going over Middlebury Gap.  I got dropped on Middlebury Gap.  Was it the bottle's fault?

The steep part of Middlebury Gap climbs 263 meters.  It took me 12:15 (shut up).    The potential energy of a water bottle at the top of Middlebury Gap is 1160 joules (relative to the base of the climb), so dragging this stupid bottle up the mountain cost me 1.625w for twelve minutes.

While this number sounds small (just like the sprint numbers), it's worth five seconds on the climb.  Was five seconds the difference between me maintaining contact and not getting dropped?  No.  But it's a non-trivial portion of the time savings I needed to stay in touch.  I could have taken the GoPro off my bike, and not ridden with a tube and pump, and used my lighter wheels, and taken about 3 pounds off my race setup.  Now we're up to 15 seconds faster...

If I could lose five pounds of old-man-metabolism fat between now and GMSR 2017... now I'm down eight pounds... at the same power I'd go over Middlebury gap 33 seconds faster... oh god this is how cyclists get eating disorders, isn't it?

...

So, uh, don't throw your bottle, ever.  But if you're gonna throw your bottle, throw it along with your spare tube and CO2 and GoPro and 5 pounds of fat, so you don't get shelled by the freaking Cat 3 field on Middlebury Gap.