Tuesday, January 6, 2009

treadmill math

here in the midst of taper week there isn't much going on as far as actually running. i've spent some time browsing the runner's world recently-renovated-and-still-full-of-bugs forums, and i'm reading both pfitz's "advanced marathoning" and daniels' "running formula" to figure out what training regime is up next. i need something hardcore that will help me get way faster. so far, they've both been good reads and i know either route will be beneficial. i'm kind leaning towards daniels' a little more, but the laziness in me likes that pfitz provides clear-cut schedules. luckily, i have a few days to read more, mull over it and decide.

i put j's engineering degree to good use with a scientific experiment on my treadmill so we could figure out what the 'real' speeds are. i know i'm not that fast, but i know what my easy pace is on average and it was not matching up to what the treadmill was reporting.

first, he measured the length of the, um, running strip thing in inches (52.5") and then multiplied it by 2 since you can only measure half of it, unless you want to flip your treadmill over and measure the underside of course but multiplying is easier (105"). he also marked a spot on the running strip to help track each rotation. then he set the speed on the treadmill, to seven different speeds ranging from 5.5 to 8.5, and timed 20 rotations (using the spot) at each speed. he did this 3 times at each speed to ensure the most accurate data of course.

now for the boring equation part:

# of rotations * length of running strip = distance (in)
20 * 105 = 2100 in

distance / time it took to reach 20 rotations = speed (in/s)
2100 / 16.36 = 128.36 in/s
(for "7.0" setting)

(speed (in/s) / 12 / 5280) * 3600 = speed (mph)
(128.36 / 12 / 5280) * 3600 = 7.29 mph

7.29 mph translates to an 8:13.9 min/mile
which is kind of like the treadmill telling you your speed is 7.0 mph (8:34.2 min/mile)

of course you do this for each of the rotation-timings and then figure out the average at each treadmill setting. on my treadmill, the actual speed was about .20-.30 mph faster than what the treadmill says. i'm just glad the results came back in my favor! i'm not as slow as the treadmill tells me i am. :o)

belated congrats to all you other lottery winners and african trust-fund inheritors out there. who knew we were all a bunch of millionaires spending our days blogging about running...

monday (1/5) pm run: 4.4 miles, 41:29 (9:25 avg pace), avg/max hr (143/164)
tuesday (1/6) pm run: 4 miles (2xmile@7:16), 33:01 (8:15 avg pace), avg/max hr (172/197)


  1. This sounds like some stupid math I would do. Glad you finally have a handle on the treadmill mystery. You can can taper in peace.

    The weather at Disney is looking quite good for this weekend.

  2. i've always wondered about accuracy of the treadmill calibration! glad you figured it out and not me ;o)

  3. RE: Goofy challenge - I have a few friends heading down there this week too. Have fun! Don't forget the 5k on Friday, right? You're already there, might as well go for the full triple nut, eh? I don't see that on your training plan (?)
    RE: treadmill - did you double check the 105" by actually measuring the tread length from the spot u marked all the way around? There may be more(or less) than you est'd around the roller which you can't see & it maybe isn't exactly 2x the topside tread.
    Also, as a long time treadmill runner I'd suggest u set the incline to 1.0 or at least 0.5 to better approximate 'real' outdoor running. The motor helps pulls the tread so the slight incline will make things even-Steven.

  4. I know that our minds go a little wacky during the taper, but bringing an innocent bystander into the madness is just wrong. LOL.

    Cool math, though.

  5. Yeah, the new RW.com is frustrating beyond belief.

    And 'not fast'? Sorry, beg to differ.

    Curious about the Daniels plan, but too lazy to research it myself. Will read your blog to hopefully find out more if you do decide to embark on it.

    (Skipped the whole treadmill part...sorry, hurt my head just looking at it)

  6. You need something hardcore. I have seen your running log and you are already hardcore and fast too.Can't wait to see your new plan. Pretty interesting about the math.

  7. haha i have done this on my treadmill too because i KNOW its off (says you are going slower than you are... so annoying). i need to do it again :) i think mine was like 5% off.

    i used pfitz for my last marathon and am going to use it again... i really liked it. cant wait to see what will be next for you! although i cant wait to see how you do this weekend first :)

  8. Can't wait to see what plan you choose... I may try something more aggressive for my fall marathon, depending on how it goes in the spring.

    Enjoy your last few days fo taper!

  9. deldean - thanks for stopping by. i'm not quite nutty enough to go for the 5k too. i think i've heard it called the "dopey" to do all 3 races. i'm sure the half and full will be more than enough to satisfy my running needs!
    also, i set the treadmill at '2.0' for the incline. i know i've heard about giving it at least a little incline to better simulate running outdoors but i didn't know all you need is .5 or 1! thanks for letting me know i can slide that number down! for the tm experiment, we measured the length from the middle of each roller, so hopefully that should account for every inch - a very valid point though. not sure how you can be a long-time tm runner! i can't handle it for too long myself :)

  10. All that math is why I don't run on treadmills. :o)

  11. I guess this is what we call taper madness. but hey, it was a great explanation and its always a good thing to find out you have been running faster than you thought you were.

  12. To...many...numbers. Make..brain...hurt.

  13. Treadmill math? Yikes.

    I can't imagine how much harder your training plan can get. GEEZ!

  14. And all of that math is why I am not an engineer! Thank J for me, for figuring out my timing issue, too, would you?

    I feel a HUGE shoutout coming on, in my blog, this evening!!! I am so excited for you for this weekend.

  15. Don't want to bust bubbles, but did you do the speed test with you on it? I have a pretty decent tread but it does slow down with me on it. Which you would still need to know to advance the speed to counteract that fact. I may have to try this myself (obviously with someone else counting the stripe).