Masters Running


Wildchild’s Theory of Running Relativity (Read 74 times)

MM #5616

    You know how in Einstein's theory of special relativity, time and distance change depending on your perspective? Well, running miles change in relative length depending on lots of variables: weather, hills, altitude, snow depth, etc.  I tried to formulate a theory to account for all the variables.  Here are my initial thoughts.  Let me know if you think these sound about right, and if I've missed any.


    Hills:  Uphills take more energy, and downhills less energy.  But they don’t cancel out – a run with equal up and down hills is harder than the same distance on flat ground.  I propose that for uphills, you add 0.1 miles for each 100 ft gain, and for downhills, you subtract 0.05 miles for every 100 feet loss.  So for a 1,000 ft climb, regardless of the distance, add a mile.  And for every 1,000 ft descent subtract 0.5 miles.  This makes the calculation easier than figuring percent grades on each section – just multiply the total net elevation gain in feet by 0.001 and that’s the extra mileage you get credit for.  And multiply the total net elevation loss by 0.0005 and subtract this from your total mileage.


    Altitude:  Sea level is for sissies!   But I think running really only gets noticeably harder above about 8,000 ft.  Some of you may have a lower threshold….      So I propose that you add 1% per 100 ft above 8,000 ft.  So a mile run at 10,000 ft counts as 1.2 miles.


    Snow:  Running in snow is harder.  There are many different kinds of snow, including hard packed, slushy, icy, or the consistency of sand, but as a general rule I propose adding 5% for every inch of snow.  So a mile in 2 inches of snow counts as 1.1 miles.  A mile in a foot of snow counts as 1.6 miles.


    Temperature:  Running in the heat is obviously harder.  For me, it starts to get harder at about 60° F.  Some of you will have different heat thresholds.  And I think the difficulty increases exponentially, so I propose that you take the degrees F above 60° and raise to the 1.2 power to get the relative percent.  So if it’s 80°F, you take (20)1.2  = 36% harder.  So a mile at 80° counts as 1.36 miles.  If it’s 100°F, a mile counts as (40)1.2 =  84% harder, so a mile counts as 1.84 miles.

    And running when it’s really cold is harder; below about 10°F you can add 2% for every degree F colder than 10.  So for zero degrees a mile counts as 1.2 miles.  -10F counts as 1.4 miles.  Most people except Erika probably won’t run when it’s colder than -10F!


    Wind:  Obviously, a headwind makes it harder and a tailwind makes it easier.  And a sideways wind is no fun either.  I propose adding 1% for every 1 mph the wind is blowing over 10 mph as a headwind, and subtracting 1% for every 1 mph over 10 mph as a tailwind.  And a sideways wind adds 0.5% for every 1 mph over 10 mph.  So with a headwind of 30 mph, a mile counts as 1.2 miles.


    Humidity:   Fortunately, I don’t have a lot of experience with humidity.  But I know when it’s hot and humid it sucks the sproink out of you.  It really has more to do with dew point than humidity. I propose that for dew points above 55°F you can add 3% per °F.  So for a dew point of 65°F you can add 30%, or a mile counts as 1.3 miles.


    Rain:  Rain doesn’t really make it harder to run, just less pleasant, and only really when it’s a cold rain.  So I propose that at temperatures below 40°F, you can add 10% if it’s raining.


    Dog Anchors:   Any of you who have ever tried to pull a dog on a leash that doesn’t want to go in the direction you’re running knows it’s like dragging a tire!  I propose you get to add 5% for every 10 lbs the dog weighs.  So for a 70 lb dog like Tazzie, I can add 35%.  So pulling Tazzie for a mile counts as 1.35 miles.


    And finally, Treadmills:    Although most people run on treadmills to avoid many of the above conditions, it’s so mind-numbing that it should count for more miles! So you can add 5% for every treadmill mile run.  So a 15 mile treadmill run counts as 15.75 miles.  And if you set the TM on an incline, you take extra credit for that based on the net elevation gain discussed under “hills.”   If you set it at 4% incline for 5 miles that’s 211 ft  per mile, or a total of 1,056 ft gain, so you get credit for an extra 1.05 miles, in addition to 25% (0.25 miles) for the treadmill run.


    Running Relativity Formula:

    For those of you who like equations:

    RD = AD + 0.001 G – 0.0005 D + AD (A/10000 + 0.05 S + T1.2/100 + 0.02 EF + 0.01 HW - 0.01 TW + 0.005 SW + 0.03 DP + 0.1 R  + 0.005 TM)

    Where RD = relative distance, miles

    AD = actual distance, miles

    G = net elevation gain, ft

    D = net elevation loss, ft

    A = altitude, in feet above 8,000 ft

    S = snow depth, inches

    T = temperature in °F above 60°F

    EF = Erika factor = temperature in °F below 10°F

    HW = headwind, mph above 10 mph

    TW = tailwind, mph above 10 mph

    SW = side wind, mph above 10 mph

    DP = dew point in °F above 55°F

    R = raining = 1 if temperature is ≤ 40°F

    TM = treadmill = 1 for each treadmill mile

    I hammered down the trail, passing rocks and trees like they were standing still.


      Ok. This is what happens when an engineer

      a) tapers

      b) is bored

      c) wants to mess with the rest of the world



      I am so geeked out right now I can't stand it. Big grin

      "He conquers who endures" - Persius
      "Every workout should have a purpose. Every purpose should link back to achieving a training objective." - Spaniel

      an amazing likeness

        Will there be an app for this?

        I've done my best to live the right way. I get up every morning and go to work each day. (for now)


        MM #405

          Big grinBig grin  Wild, you are so cool.....I can`t wait to meet you!


          (..What kind of dog is Tazzie )



          MM #5615

            It's going to take me the whole month of March to calculate my February miles.

              ...Factor in' ' DeepWater'' and I think you're onto something.......

              ..nothing takes the place of persistence.....

              MM #6177

                Will there be an app for this?


                Trails are hard!

                  I noticed that most of those factors seem to be relevant to your normal runs.  don't you run enough miles as it is? Joking


                  And I totally agree with C-R, too.

                  Need a fast half for late fall.  Then I need to actually train for it.


                  MM #6177

                    Oh, and I take issue with your "sea level is for sissies" assertion! Considering some of us don't have a choice about running at sea level, I think that's a bit unfair... and anything over 60F is too hot?? How about over 90F?? What are you going to say now, that running on paved roads decreases the "theoretical" mileage?


                    Big grin


                      And don't forget age. We 'old' people want to be factored in also!


                        What about the Ilene factor, for me each of my miles counts as 1.25 of your miles.  Big grin


                        Running is stupid

                          Absolutely!  Each & every weighting factor is spot on!

                            I think us taller runners should get a factor too.....I've got extra height (and therefore weight) on a lot of you shrimps, so don't I get credit for that?  Plus, I think your sideways wind is a bit off.  If it is a hot day, the sideways wind cools you down, so it cancels out some of the heat factor.  Gosh, you really could get sucked into thinking about this too much.  How about just looking at avg HR!!!! and if it is higher than normal, you can multiply that..... HRnewrun/HRusualrun X mileage of run = effective mileage for new run

                            "During a marathon, I run about two-thirds of the time. That's plenty." - Margaret Davis, 85 Ed Whitlock regarding his 2:54:48 marathon at age 73, "That was a good day. It was never a struggle."

                              . . . . my brain is cramping . . . . .

                              Living and Running Behind the Redwood Curtain


                              Trail Runner Nation


                              2018: Mendocino Coast 50k - April 21

                              Back on Stride

                                Will there be an app for this?

                                How many of you have Android smartphones? I could whip this up as an app within a day or two, although the general app-loading public on the Google Play App Store might not react well to it. Wink


                                And it does look like Carolyn is trying to pad her runs, turning a 10-miler into a 20-miler with all the correction factors, leaving us sea-level flatlanders probably with negative corrections. Unfair (but I like it!).


                                Next thing you know, she'll be factoring in the relativistic time dilation factor...

                                Doug, Runnin' in Rochester, MI