Running Lessons from Isaac Newton

Posted by Filed Under: Weight Loss

A while back, CRN co-founder Mark posed the question to me: “Hey, Bill? How does having lost weight change my running? As in: I know it makes me faster, but can you quantify that?”

Being an engineer, I was tempted to snap back that I’d spent four years and a decent part of my potential life’s income learning how to answer those questions. Then, I was afraid that all that knowledge had slipped under the bridge, and I wouldn’t actually be able to answer the question…

Ah, but fear not, readers – the years and the beers haven’t completely eroded Physics 101. In fact, thanks to good old aerobic exercise, I’m likely smarter now than back in college when my exercise regime consisted largely of 12 oz curls.

newton.pngWe’ll start at the beginning, with Newton’s famous

F = M * A

or, Force = Mass times Acceleration.

Rearrange this a bit, and we can see that

Acceleration = Force divided by Mass (A = F / M )

So, off the line, dropping, say, 15 lbs off of a 150 lb frame will make you able to accelerate 10% faster, assuming that none of the weight loss came out of muscle tissue.

There’s a similar benefit to be had in climbing—climbing is just vertical acceleration, with the earth’s gravity trying to pull you down with a constant acceleration of 9.8 meters / second squared. Weight reduction means that you can climb at the same rate using less force where the rubber meets the road.

I’m sure that everyone has heard Newton’s other law about “An object in motion tends to stay in motion until acted upon by an external force”. Well, strictly speaking, that’s true. However, we’ve got plenty of external forces to deal with. There’s wind drag, which we’ll deal with later, but more importantly, there’s gravity.

For those of us in the real world, we really aren’t moving straight forward as we run. In reality, we’re tracing a series of arcs as we push off with one foot, raise our center of gravity up as we push off, experience a brief bit of weightlessness at the top of each stride, get pulled back down to earth by gravity, foot strike, store energy in our legs, and push off again (Yes, yes, Mr. Pose—as much as we try to float our feet in circles, there is still effort involved).

Every time we push off to enjoy that delicious moment of weightlessness in each stride, we’re doing work. In the engineering sense, Work is defined as Force over a distance. In our case, each step involves the work needed to lift up our bodies enough to swap feet, and enough work to overcome hills and aerodynamic drag.

Assuming that drag remains constant regardless of weight (a bad assumption, as cross-section goes down as we get skinny, but I don’t feel like hitting Wikipedia for that one), with each step we’re going to have to lift our body up. 10 percent weight reduction means that each step we’re doing requires 10 percent less work with each step, requiring 10 percent less power (work times time) to maintain a given velocity.

OR, again, with the assumption that you’re not losing power as you lose weight, you can go faster with the same amount of muscles if you’re skinnier.

Picture it this way: Say you lose 5 pounds. Five pounds is about the same as a half-gallon of milk. I were to ask you to lift a thousand half-gallons of milk onto a 6″ stair, you’d think it was a tough, tough task. Losing five pounds is like not having to lift that 500 gallons of milk in every mile you run.
Editors Note: Whether you should lose weight or not is something you should discuss with a professional such as your doctor or coach. We do not advocate that athletes try to lose weight just to get faster.

About Bill Jankowski

Jank is the nom-de-plume (alias) of Bill Jankowski. Jank is a runner (defined as “one who runs”, without any necessary claims of athleticism). More accurate would be to say that he enjoys the company of his iPod, and goes to great lengths to get long periods of time alone with his thoughts. Plus, running is a wonderful way to keep his ego in check. He’s been physically active since he was a kid (assuming that, for the years 1995-1999 and 2001-2003, drinking counts as “active”), playing Soccer, Flag Football, Basketball, and Softball while in college (for his fraternity’s B-team)(Actually, add 1990-1994 to the years of inactivity). In addition to running, Jank swims (controlled drowning), bikes (’cause his mom suggested he play in traffic as a kid), and kayaks (see swimming, but with sharks and props). An engineer by the grace of God, a (recovering) submariner by the graces of the taxpayers of the United States, and an MBA by mistake, Bill enjoys gear (oooh, shiny!), cycling (oooh, shiny bikes and clothes!), and poking at accepted ideas with a pointy stick. In 2004, Jank decided he didn’t want to go full-over to being fat, and took up running (instead of stopping eating). In 2005, he finished his first marathon (WooHoo!) in October, and his second two weeks later (dumb idea). He is still recovering. Bill lives in Connecticut (the poorer, eastern part) with his lovely wife Melissa (who is far more fit than he is and way less navel-gazing about it), and their two sons, Jake and Nate, who, in addition to having deliberately cool names, are the finest children to grace the Earth (clear proof that “evolution through natural selection” is bunk; although he still questions the monthly bill for “Pool Boy” despite not having a swimming pool). His rants can be found at; his best stuff is found here at CRN.

  1. Blaine Moore (Run to Win) on June 26th at 10:30 am

    I don’t think that the editor’s note should only apply to young athletes. Remember that there is a rule of diminishing returns; once you reach a certain point, additional weight loss is going to mean that you can not exert the same forces as you could with that weight, be it through muscle tissue or early fatigue.

    The ideal should be to reach and maintain a healthy weight for your body frame and your lifestyle, not to always lose weight no matter the cost.

  2. Mark Iocchelli on June 26th at 11:31 am

    good point, Blaine. I’ve removed the word “young” from the note. Thanks. The note was originally intended for young people because in another post, someone had concern about us not warning high school girls not to lose weight just to get faster. However, the same logic definitely applies to runners of all ages.

  3. Blaine Moore (Run to Win) on June 26th at 3:12 pm

    Yeah, I was thinking of that article. I know what it is like for myself to lose weight, though, and I definately do not have a better situation. I am pretty much at my ideal weight for what I do.

  4. billjank on June 26th at 3:42 pm

    I suppose I should have specified that I was directing my comments towards fitness runners, not necessarily “finely tuned atheletes on the verge of greatness”. Picturing myself, and most of the folks I run with, there’s not a one of us in danger of losing muscle mass.

  5. Amy on June 29th at 2:23 pm

    Great reminder! While in no way as scientific as your explanation, I learned this one by carrying around my kids as babies. I would haul them around (sometimes 20 lbs) and then after I would put them down and go for a run, I would think – “gee, this is easier, what would happen if I could lose the 25 lbs I need to get back to normal.”