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To run or to run/walk…that is the question *December 2, 2012*

*Posted by mareserinitatis in math, physics, running.*

Tags: distance, integrals, jingle bell run, running, speed, velocity

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Tags: distance, integrals, jingle bell run, running, speed, velocity

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Yesterday was the Jingle Bell Run. It’s a 5k that doubles as a fundraiser for the Arthritis Foundation. My team did fairly well for fundraising, coming in 6th place overall. This is rather impressive because our team had 3 people, and all the groups ahead of us had at least ten. If they had averaged it out per person, we definitely had the highest donations per teammate. One of my teammates was the second highest fundraiser overall…and got a certificate for an hour massage.

We got to wear elf costumage while running. How cool is that? (And no, Gigadog didn’t run. I attempted to a couple times, but after almost faceplanting when the leash got tangled around my legs, I didn’t feel like I could keep training with her.)

Actually, we were worried that we were going to be overdressed, but it turned out that people go all out for the race. There were elves galore and many wearing santa hats. There were also people dressed in costumes – angels, reindeer, christmas trees, and even full-blown nativity scenes complete with puppy dogs dressed in lamb’s clothing. (The owners were dressed as shepherds.)

All in all, a good time.

An interesting conversation occurred later, however, when we talked about running versus running/walking. Last year, when I started running, my goal was to run a 10k straight through. I managed to do that, but I noticed my progress was rather slow. This year, I’ve started using a program where I do running and walking intervals, and I’m noticing a huge difference: my rate of improvement has really increased from month to month. The topic came up with a friend’s husband, who said it just makes more sense to run straight through. He had a hard time believing me when I said I could actually go faster with walking breaks.

An easy way to see this is with a graph:

Unfortunately, my legend got scrubbed, but what we have are actual speeds from different exercise sessions I’ve done. (Yes, I know I’m slow…but I needed data.) The blue comes from near the end of the race yesterday, while the green is from a timing run I did (no walking) a couple weeks ago.

If you’ve taken basic physics, you know that the integral of the velocity over time gives you the distance. For those who don’t know calculus (or integrals), and easy way to see this is to look at the area of the bars. You can see that the area of the two blue bars together is greater than the area of the two green bars together.

Another way we can think about it is to calculate distance over an hour. The speed shown by the green bars is 4 mph. In one hour, assuming I can maintain this pace, I will travel 4 miles in that hour. However, if I run half an hour at 5.5 mph and walk the other half at 3.5 mph, those distances will be 2.75 miles and 1.75 miles and will sum to 4.5 miles. While this isn’t a lot faster, it’s a noticeable difference.

Apparently running faster for half the time does more to improve my speed than running the same time interval with a slower pace.

I’m sure hoping so, anyway. I signed up to do a half marathon next spring, and I’ve gone from hoping I can finish in less than four hours to wondering if I’ll be able to make it in three. Keep your fingers crossed for me.

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