The Road to the Tevis Cup, Post #4: How to calculate the grade of hills

One of the best things about where I’m living now is that I can go out a back gate onto a very hilly cattle ranch. I grew up around here, so it’s nothing new, but having lived the last seven years in Oklahoma, I have a new appreciation for the terrain. Having started doing endurance since I left California, I also have a new need to understand exactly how much work my horse has done. Today I figured out how to calculate the grade of hills so I can better assess the effort required for the climbs we are making.

Table of contents

Definitions
What you need to calculate the grade
How to calculate grade
Why calculate grade?
Example 2

Definitions:

Elevation: height above sea level. This is the one we’re interested in because changes in elevation mean more work for the horse. Not to be confused with…

Altitude: vertical distance from the earth’s surface. If your altitude is varying much while you are riding, you’ve got some training problems.

Rise: Change in elevation (highest point – lowest point).

Grade or gradient: This is what we see on roads when people are worried about semis running away (going down) or overheating (going up). It’s usually expressed as a percentage, and, in the USA, in feet. It is the slope (m = y/x), or rise (elevation gain)/run (distance).

or

Gain: Increase in elevation per unit of distance. For example, if you want to know how much elevation you gain in one mile, divide the elevation change (highest point – lowest point) by the distance. This is exactly the same concept as grade, but not expressed as a percentage.

One mile = 5,280 feet = 1,609 meters (1.609 kilometers)

What you need to calculate the grade:

All you need to calculate gain, rise, and grade is the elevation at the bottom and the top of your climb, and the distance covered.

Elevation

There probably many apps that allow you to record your elevation, but I use GAIA. Unfortunately, it does not have a “horseback riding” option, but I’ve been using it for hiking for a while. It’s very accurate, and the topographical maps are useful when you are trying to transverse mountainous terrain.

To mark exactly where your climb begins and ends, you can add “Waypoints” to your GAIA map. I also use these as trail markers when there are no good land marks. Waypoints save your coordinates and elevation.

You can also use a GPS camera app (there are many). These record your precise location (latitude and longitude). You can then plug in the coordinates on various websites to find the elevation.

There might be elevation apps that allow you to save your location and/or a specific coordinate too.

You can guestimate with Mapmyrun. It does have a horseback riding option! If you know the approximate “shape” of your ride, you can use the elevation feature to take note of the highest and lowest points of the climb in question. Mapmyrun is not very accurate in mountainous terrain however, so it probably won’t be as precise as other options.

Of course, a Garmin will also provide elevation and distance data and can be used to set routes and waypoints. I don’t have one (although I really want this Garmin Inreach, which allows satellite communication), so I cannot provide details on use. (Note: I ended up buying this Garmin Fenix 5S. I’m very happy with it so far!)

Distance

Unfortunately, GAIA does not provide the distance between waypoints. You can calculate it roughly after-the-fact by long-clicking that portion of your trail, but unless you go in very straight lines, this is a pain. Easier to take screenshots (of your mileage) and do a little addition and subtraction.

To calculate grade, you need the distance (run) in feet. Most apps provide distance in miles or kilometers. One mile = 5,280 feet = 1,609 meters (1.609km).

For example, one of the hills I climb with Fantazia involves a distance about 0.52 miles. To convert that to feet, I would multiply: 0.52 miles*5,280 feet/mile = 2,745.6 feet.

Devices

Obviously, you need a smartphone or Garmin or similar to track your movement. You also need a calculator (or app) unless you are a real glutton for punishment.

This website allows you to input coordinates and gives you the corresponding elevation (very useful) as well as the grade between the two points as the crow flies. This isn’t very useful unless you are riding straight up a hill.

How to calculate grade

Formula: Grade = (elevation change/distance)*100.

Rise or Elevation change: Almost all apps will give you elevation in feet, so simply subtract lowest point from highest point.

Taking the hill I mentioned before as an example: Highest point = (approximately) 1,528 feet. Lowest point = 1,167 feet. Change = 1,528 – 1,167 = 361 feet.

The distance along the road we climb is about half a mile. We calculated it in feet above (2,745.6 feet).

Grade: 361/2745.6*100 = 13.15 or 13.15%.

The website mentioned above calculates a grade of 25.5%. That would be as the bird flies (there is no other way to go straight in this country). On average, because even if you went straight, there would be (mainly) ups and (a few) downs. Of course, even my calculation is approximate, because in fact, the road winds up and down. There isn’t much down, but there is a bit.

What about gain?

Not really as useful.

Gain per mile = 361/0.52 = 694 feet per mile. Gain per foot = 361/2745.6 = 0.1315… So for every foot ridden, you go up 0.1315 feet, or just over an inch and a half.

That’s fairly useless information, even on a longer ride. For example, the ~10 hike from my boyfriend’s house to my parents house involves climbing slightly over 1000 feet. (Overall gain per mile = 100 feet.) It’s much more useful to look at the output on GAIA which tells me that when we did that hike, we climbed a total of 2,186 feet (and descended a total of 1,214 feet). It’s very hilly, even when we do our best not to lose elevation.

Why calculate grade?

However, for endurance conditioning, it can be useful to know how to calculate the grade of the different hills you have to condition on. Besides the one mentioned above, there are two more fairly tough hills on the property adjacent to ours. Theoretically I could judge which one to tackle at a higher speeds according to grade. In reality, the toughest is so technical there isn’t a lot of room for speed.

Better yet, there are many climbs of various steepness and difficulty in the large cattle ranch to the west. I will want to calculate grade for many of these. It’s difficult to tell just by eyeballing them which is going to be the most challenging.

Example 2

Today I rode up a short, steep hill that was pretty much a straight line (video below). I had planned to use GAIA to place waypoints, but my GAIA app glitched. It did not follow my trail. However, I could use it for elevation by taking screenshots at the top (1368′) and bottom (1215′) of the slope. (**not the true top, just as far as we went today).

Elevation gain/rise: 1368-1215 = 153 feet

Distance: I glanced at mapmyrun to gauge distance (subtracting end from starting point): 0.10 miles or 528 feet (0.1*5,280).

Grade: 153/528*100 = 28.98 or 28.98%. Very steep. I dismounted and led Fantazia down.

Related posts:

Prerequisites for riding the Sierra Nevada is all about what your horse should know before tackling these hills.

Previous Road to Tevis posts:

Introducing Fantazia

Fantazia’s first three weeks

Post #3: When I met Fantazia

Next post:

The manure fork incident