It's always the big debate at championship courses, should there be hills? Should it be flat? What should we do? People want flat courses because they want to go fast. But coaches sometimes like the hilly courses because they serve certain athletes better than others. And, frankly, having a challenge is always a little bit fun. I'm Jesse Funk and on today's episode of Runner's High, I'm going to talk to you about a few calculations people smarter than me have figured out about how hills affect our running speed.

If you build me here on the channel for any period of time, you know that recently I flew out to Colorado Springs to run the incline to actually Manitou Springs. It is a trail run a little less than a mile and it climbs 2,000 feet in that time. Because I had no idea of what the implications of that kind of run would be, Iâ€™d never run anything of that magnitude, I started to pour over the numbers. If you haven't seen that video, hit that subscribe button, in the bottom right hand corner and go check that out after this video.

But I started to try to figure out, how is this climb going to affect my speed? What is it going to do to me, and I found a couple calculations that actually pertain to the gradient change and our base speed and how that affects how fast we're going to go. What I came up with were two very different approaches to this problem of figuring out how that hill gradient change changes our running time.

These are by two coaches, our beloved community running coach Jack Daniels, who I often refer to and also coach John Kellogg, who you might know from the Let's Run forum. Danielâ€™s formula takes into account a uphill and downhill change, and does it differently. He says for every percent gradient change uphill, we're going to lose 12 to 15 seconds. Every percent change downhill, we're going to gain back around eight seconds.

This is nice because we know going uphill, we're going to lose more time then when we go downhill, just like when we're in a headwind versus a tailwind, we lose more time in a headwind than we gain in a tailwind; more particular to cycling, but it also has a little bit of play in running. Kellog, on the other hand, doesn't take into account the up or down, and gives us more of a rule of thumb. It says for every 10 feet of elevation change regardless of direction, we change our speed, basically, by 1.74 seconds.

Now, as a rule of thumb, I would actually probably say, let's do two seconds, so it's easier mental math, and then we can adjust from there, it's going to get you pretty close within a margin of error most of the time, but that's, you know, if you're looking at a Course Map, that's kind of the quick way to do it. Say the Course Map says so repeat, then you know you multiple by two and figure out what your change in time is.

Personally as kind of a math nerd I prefer Daniels formula because it's a little bit more precise in that it counts for both uphill and downhill separately. But I can't help but love Kellogg's simplicity, if we change it that two seconds, because of how easy it is. So, say we have 100 feet of climbing, well, then we have to divide that by 10. It's going to be 10 times two, that's 20 seconds.

And actually, what you end up doing is because it's 1%, ?? 3:31> instead of two, we can take off roughly 10%, which makes it 18 seconds in change. Well, the actual answer here is 17.4 seconds. But multiplying by two is much much simpler than multiplying by 1.74 especially when we have not nice numbers.

I believe these formulas are very, very useful for most courses we're going to run into, but they do have a limit. And that limit comes into play on something like the incline where they don't really apply very well. So, let's use Joe Gray as an example. Joe Gray is the kind of uncontested fastest known time on the incline, his time was 17:45. Now, let's also know that his fastest 5K time, the least that I could find is 14:12. Now, you may be thinking, okay, the incline is just about a mile long. So, what should we use his mile time is our base?

Well, I'm using a little bit of intuition here and saying that the incline effort is roughly the same length time wise as a 5K. So, I want to use Joe's 5K, mile time, mile split as it is, as our base time instead of using his fastest mile time and then making adjustments because you know what, say Joe can run low fours. Well, he can't hold up that kind of effort for 17 minutes in his particular case. So, it doesn't really make sense to use a mile tend, so weâ€™re going to use that base time from is 5K, and then make the adjustments using Daniels formula and see what we get.

The relevant numbers for us here, the incline is .88 miles. Now because we're trying to use some calculation, I always like to try to build in wiggle room. So, let's just assume that the incline is a full mile long. That way we can kind of try to account for the change in altitude, climbâ€™s 2,000 feet. It starts at 6,500 feet, goes up to 500 feet, I have a whole other video on altitude change how that affects us.

So, if you haven't seen that, as always subscribe to the channel. But we have to take that into account. So, let's pretend it's a mile long, the average gradient change is 43%. So, that's going to come into our calculation taking that 43 by Danielâ€™s rule 12 to 15 seconds, and the average mile split in Joe's 5K time is for 38.

So, if we take, let's say 15 seconds instead of 12, again, I like to try to give a little bit of wiggle room, and we know that the incline is a very, very difficult run. 15 seconds times 43, we end up with an additional 10 minutes and 45 seconds. We add that onto Joe's base time we end up with 15:23. As you can see, this calculation has its limits, Joe ran 17:45, nearly two and a half minutes slower than what his supposed fastest time can be.

Two and a half minutes is a lot especially at that kind of range. It's like saying, saying that he runs a 17:45 5K and he can take two and a half minutes off just through perseverance. I think maybe Joe has a faster time in him, but two and a half minutes is a bit of a stretch. So, this is a good example of how this calculation has limits. Even Danielâ€™s version has limits.

So, any kind of course where you're gonna have up to say 10% gradient change, and this is kind of just a guess, an intuition based on my experience, these formulas are going to be a pretty good, reliable indicator of how your speed will change over the course, based on this gradient changes. But anytime you get into something more extreme like the incline, then it's going to be much more difficult to predict the actual outcome because you get to a point where you can't actually run anymore, it is more walking and using your hands to scramble at some points, because that trail is so extreme.

As always, that button right there, or maybe it's right there ?? 7:40> my backwards video together. Hit that subscribe button, stick around me for more tips on running, running faster, running better, being the best runner you can possibly be. I'll see you next time on the next episode of Runnerâ€™s High.