Hi Friends, if ever you were self conscious about sending us your articles fear no more! For I am going to fall on my sword and set a precedent in “things that I wouldn’t want known by the public so I’ll keep them to myself” by making my dubious math skills public! It can only go up from here y’all!

So in honor of this month’s theme (that I made up) I wrote an article about what I love about running. And what I love is music, or rather being able to incorporate music into my running. It’s a great time for me to jam to some bops and not have to worry about anything or anyone else, or anyone’s unsolicited and incorrect comments about my musical tastes. I also find that it helps me through tougher segments or tougher days when I can center myself on the beat of the song and as I have mentioned before, I have certain songs for certain challenges like speed work, hills, tempo, etc. BUT I thought why not take this a step further and utilize my love of music to optimize my runs for achieving certain paces? All I thought I would need to know is what beats per minute (bpm) equates to what minutes per mile. Easy right?

As it turns out, no, it isn’t quite so simple. I mean yes there are some averages and guidelines out there but I am a scientist, at least according to my W2, and I need tests and data to back it up. So I went a researching to find out what I needed. Basically I needed to know how much distance I would cover in a single beat, in this case 1 step, how many steps it would take to reach 1 mile, and then in order to achieve a certain pace, how many steps per minute aka bpm. But I also didn’t want to just calculate it for myself, because if this was helpful I wanted to be able to share it with you cool kids. So I looked up the largest factor determining your step length and while there are actually a LOT of factors, height is usually the primary. So I looked for a quick way to estimate your step length (though they refer to it as stride length) by height in order to make a chart. Turns out there is some disagreement on what that is. In the 1970s they determined that a person’s stride length is roughly 1.14-1.17 times their height but a more recent study couched it closer to 1.35. There was also some disagreement on what a stride was i.e. 1 step or 2 steps (this will come up later). Anyway I decided to go with the more conservative number of 1.15 and made up a calculator to estimate the BPM required by height for each desired pace which can be found here in its original form: https://docs.google.com/spreadsheets/d/1lIgFPXMSQ6kXbecqzSZ_VsHidtDH8BZOCRE3Q8MxOV8/edit?usp=sharing

But as I mentioned, I am a scientist by trade and science is about making a statement, doing a test to back it up, getting cold hard data, analyzing your results, and doing it again to confirm your findings. I mean in reality, usually the “do it again” part is because our first results are confusing and we think we messed up somewhere (like in the maths) and need a sanity check before we make a fool of ourselves but that’s neither here nor there. 

So what did I do? Well I crafted myself a playlist using this handy website: https://getsongbpm.com with 5 songs of varying BPMs that according to my calculations would allow me to achieve 11:00,10:45,10:30,10:15, and 10:00 minute mile times. I then found a flatish stretch in Hanover by CRREL with stable landmarks I could use as start and finish points, put each song on repeat, and using my innate sense of rhythm ran exactly one mile (according to my watch) on the same course, for every song making sure my footfalls lined up with the beat. I then threw in a 6th song just for funsies that I didn’t know the BPM of and wanted to see how close it would get to my calculations. Below is a table of my results which are…interesting

As you can see, my calculations were LUDICROUSLY off by a good 2 minutes and some change. I pretty much knew immediately when I started running to the first song that something was up, but I decided to roll with it and not look at my watch until the end so I wouldn’t bias the results and after that it was just fascinating. I’m just glad I didn’t try to test the faster paces because I think that would have killed me. Anyway, clearly the numbers just didn’t add up, I needed more data, and fortunately we live in a data renaissance and I could pull oodles of data from Strava (thank you) and my Garmin watch. Below are the 5 songs (and my 6th song which was the wild card)

What I find interesting here is that my total steps are all over the place and not really correlated to pace BUT my actual stride length was relatively consistent and primarily got longer when the pace increased by a minute which makes sense. Also I’m pretty proud to say that my cadence was pretty darn close to the bpm *brushes shoulders off*. Now here is where it gets kinda cool. So given that my watch treats 1 stride as 1 step, I multiplied it by 2 for simplicity to arrive at my “2-step stride” and then I calculated the conversion factor from my height to my stride length and found that it was actually about 1.35! Which if you’ll remember from earlier was what “some” sources had estimated as well. I thought that was pretty cool BUT I wasn’t done yet. Using this new conversion factor I redid my calculations (available here: https://docs.google.com/spreadsheets/d/1phe4Qrp3PFswF4619OgzjGJNb33xekuW65xhbdY_118/edit?usp=sharing) and found that the new estimated BPMs to get the paces that I actually got were MUCH closer, see below

And there are of course a bunch of caveats with this whole experiment that influence our pace when we run. For starters like most recreational runs, the surface was not actually consistent nor completely flat. I found that on my way back after turning at the halfway point that I was running into the wind and though I was able to keep the pace, I definitely felt my momentum lagging. I also got colder as I ran for a bit so my body moved differently. And as I noted earlier, at the faster paces I pseudo-consciously changed my stride length to compensate because this is my normal strategy, some people take shorter steps faster in comparison.

But what have I learned? Well first off this was a ton of fun! I loved going through all the music to find ones that I liked that could fit the paces I was after and I spent a great deal of time looking at some of my favorite songs to figure out what their BPM was and where that could fit into my pace goals. I also realized how pace aware I have become since I started running. I had a pretty good idea of my actual pace without looking at my watch which I think has come from experience (yay!) and was surprised to see how close I was everytime. And when I was focusing on it intentionally I could feel what bpms and paces were comfortable and could be like ah yes this is what I would normally consider “race pace” or “talking pace”. Anyway it was a neat exercise and I can’t wait to make more playlists for goal paces to see if the music can help me get there! And if running with music is your jam, why not take my calculations for a spin? Find a song that suits your pace, and go for it! But before you do, please consider the following disclaimers

Disclaimers

If I put it in bold it makes it seem more official. First off I am not a doctor, medical or otherwise. I do not have professional training in kinesiology, sport medicine, etc; I just have opinions and some data, not sanctioned advice, so take everything at face value. Everybody and every body is different. All the calculations I did are just estimates and there are many factors that change how an individual runs, so don’t necessarily try to match yourself up to the numbers here or elsewhere. While keeping track of your strides and stride length is a good way to run consistently, do not force yourself to achieve a certain stride length. As with everything, listen to your body and SLOWLY make changes to see what feels right. Have fun, be safe, and I cannot stress this enough: Do. Not. Make. Sudden. Changes. In. Your. Runs!