The Mathematics of Hills (and Some Racing)

Ok, I'm sure the fun-filled title of this post is what brought you here, but I'm going to cover a couple other topics before I get into the high school math refresher.

A couple days ago (Saturday, May 10) was the 5Peaks race out at Golden Ears. It was (essentially) the race director debut for my friends Solana and Jay. Let me just say that they did an amazing job. It takes a big crew to put on a 5Peaks event, so thanks to all the volunteers too.

On Friday, the day before the race, a few of us met out at Golden Ears to flag the course. The rain held off, and we managed to get all the marking done in about 2 hours. I actually enjoyed the walk, and got to meet/know Dan as we hiked and set our section of the course. The only glitch to the process was that we were short a couple 'GO STRAIGHT' signs, that i felt would help avoid confusion at important intersections. So, I grabbed a few extra signs for the next morning. I always do a long warm up before these short races, so I planned to just place the extra signs  during my pre-race run the next morning.

I showed up early on Saturday and headed out for my warm up run... only to find that someone had 'jokingly' messed with the course marking over night. Luckily, I had ran far enough onto the course to see it.

I got it all sorted out, and had plenty of time to get back to the start to meet my girls before their race. We ran around for a few minutes to get them warmed up, and they were more than ready to tackle the 1km kids run. I am so proud of them. I can't really even put it into words.....so here are a couple photos.

As you can see, they had a blast! After a round of hugs and kisses when they crossed the finish line, I got back to my own race prep.

I put on my race kit and stared doing some strides. Right away, I knew that I had some really good legs, and that I wanted to run hard! Seeing both Shaun and Jordan at the start line, pretty much guaranteed that I was in for a tough race. I have raced Shaun many times before. He is amazingly strong on the uphills, and I was pretty sure that he would put some time on me up the Incline Hill. My goal was obviously to try and take it all back on the downhills. Jordan and I have similar strengths. Which meant that I expected him to be close to me the entire race: no room to make a mistake.

Shaun leading over one of the many creek crossing in Golden Ears

Shaun leading over one of the many creek crossing in Golden Ears

The three of us ran together for the first quarter of the race, then just as I expected, Shaun took the lead on Incline. Jordan dropped back a bit, but i knew he wasn't out of the mix. I hammered the long downhill, and got back to within a few seconds of Shaun before we hit the second climb. But then again, he started to put a bit of a gap on me as we climbed. I stayed extremely focussed, and as soon as the trail turned downhill, I pinned it. I was very much on the edge, trying to pullback seconds wherever I could. Every once in a while I would catch a glimpse of Shaun ahead on the twisty trail, fuelling me to keep my foot on the gas. With about 400m to go, we popped out onto a wide open, straight gravel road. I was about 50m behind Shaun and I was fully red-lined. I gave everything that I had left just to close the gap. Right as we got to the last creek crossing, he saw that I was closing on him, and he threw it into over-drive. I had burnt all my matches to catch him, and just didn't have the legs left to go with him when he kicked. I started to tie up pretty badly, as he pulled away for the win. I crossed several seconds later, and maybe only 30 seconds after me was Jordan. It was a tight race for sure!

I am really happy with how I raced. I was really tough (mentally and physically), and actually had fun trying to chase Shaun down. I had nothing left at the end, and was happy to see that my fitness is right on track. I was more than a minute quicker than last year (when I won), even though the trail conditions were a fair bit worse this year

me, Shaun, Jordan. (I guess I should have taken my  toque off)

me, Shaun, Jordan. (I guess I should have taken my  toque off)

Check out the race day photos by Rob Shaer here.

I have to say that Saturday was one of the best family race/adventure days we have had. Even though it started off wet, my whole family had a great time. How could the weekend get better???

Well....Sunday morning was the (third) Tuff Kid challenge, held at Queen Elizabeth Park in Vancouver. It's a family focussed, kid-only 'race', that involves both running and obstacles. Dave and Megan, owners of Distance Runwear , organize and put on the event. I think their concept is amazing, and a great way to get families involved in running.

Me and the monkeys doing a warm up

Me and the monkeys doing a warm up

Given' er

Given' er

Look at that technique...and focus (hahaha)

Look at that technique...and focus (hahaha)

There wasn't a single person (adult or child) that wasn't smiling ear to ear at the Tuff Kid event. It was a perfect start to Mothers Day for us, and the sense of accomplishment (and pride) that my girls earned this weekend was priceless. I am so excited about getting in some regular (all be it, short) runs with them over the summer.

Ok, now as promised...some math: 

If runner A (lets call him Shaun) runs up a 1km long hill at 10 km/hr, it will take him 6:00 .

If runner B (lets call him Mike) runs up the same 1km hill, but at 9km/hr (10% slower than Shaun), it will take him 6:40. (Note the :40 difference)

Now, in a second scenario:

If runner B runs down a 1km hill at 20km/hr, it will take him 3:00.

If runner A runs down the same 1km hill, but at 18km/hr (10% slower than Mike), it will take him 3:20. (Note the :20 difference)

Conclusion:

Given the longer time spent ascending, compared to descending (on a given hill), climbing performance provides a more heavily weighted outcome advantage.

Therefore, runner B was screwed !!