Lollipops and Spaghetti

How many of you think about the topology of your routes, be they running, skiing, biking? Are you content with out-and-backs? Laps around a circuit? Or do you like to cover some distance and the only place you see twice is where you started? I've always preferred single big loop routes, whether it be training, racing or just heading out for pure enjoyment. After reading Racin' Rick's post about the dreaded out-and-back, I thought a bit about this from an analytical perspective.

My favorite races this year were single, monster loop affairs that cover serious terrain. Some of these were the Battenkill road race, Ironcross CX and the Vermont 50. These races boast about their single loop epicness. You don't do laps around a circuit, you don't see anything twice.

I strive for the same in most of my riding and skiing. My favorite loop on the planet is the Monarch Crest Trail in Colorado. A 54 mile loop that encompasses many thousands of acres. At Waterville Valley, I love doing a perimiter loop on skis. This just so happens to hit all the high points on the trail system, and it encloses a lot of terrain in the middle.

Engineers love figures of merit, often abbreviated FOM. A great FOM that applies here is the Isoperimetric Quotient, or IQ. Not making this up. Follow the link.  Basically, in Euclidean geometry, a perfect circle encloses the most area for the least perimeter. In terms of riding, a circularly shaped route will enclose the most land for a given distance travelled. Thus if you want to continually see as new of stuff as possible the whole time you are riding, pick routes that have a circular shape to them. The IQ is normalized to the circle, so IQ = 1, or 100% for a circle. So let's look at other, non-circular ride formats.

The Out-n-back.  I generally dread these like Rick. Sometimes they are unavoidable, like hillclimbs. In these special cases, I'll suffer through a return descent, as the reward is the summit. Trail out and backs suck, road out and backs suck even more. A lot of tri-guys do out and backs on their tricked out bikes. I don't understand this.  The IQ is zero for these rides, as no area is encompassed by the route.

The Lollipop Loop.  I will do lollipop shaped rides once in a while, especially if the lollipop stick is short relative to the yummy part. If we assume the stick is equal to the diameter of the yummy part, we get an IQ of 58%. This is an infinite improvement over the out and back, but only a little better than half that of perfect circle. This means you are only encompassing about half the area you could for the distance you are riding, and almost half the ride is seen twice.

Triangle. The triangle is another possible ride shape. Some of my work lunch rides might be triangularly shaped, where I head out a ways, cut over an equal ways, then come back an equal ways. Not a bad deal in IQ terms, were a 70% efficiency of a circle is achieved.

Square. I can think of a couple rides I like that have square shape to them. Often, these are where I go up and over a mountain range, traverse over in the valley, then come back up and over the same mountain range at a different gap, finishing with a traverse back to my car. Riders that do two gaps of Vermont 6-gaps could encounter a square shaped topology to their ride. A ride I did in Silverton, CO this summer had a square-ish shape to it too. Getting much closer to a circle's efficiency here, with IQ = 78%.

No ride will be a perfect square or circle. But you get the idea. Simple shapes encompass the most area and have the potential to present the most scenery. These rides give you a greater sense of accomplishment. You could go to the Londonderry Track and ride 300m laps all day. It is nearly circular. But you'd have to divide the IQ of 100% by N, where N is number of laps. In an hour, your IQ would be down to about 1%. This spells retahded. Similarly for circuit road races. You might have a 10 mile circuit, do it five times for a 50 mile race, but end of with an IQ of 20% or less.

Some of you techie trail riders may say wait a minute HJ, you're missing the point. Some of the best rides out there wiggle and squiggle all over the place and never go any where! Non-squiggly routes follow boring fire roads anyway and don't seek out interesting features.  This brings us to one more route topology.

The Spaghetti Loop. The FOMBA trails near Manchester, NH are a prime example. FOMBA had some unique constraints to work within, namely having very limited acreage to build unlimited trails in. The IQ for some of these trail segments might actually be negative, as you come close to the same point many times. The distance travelled is large, but you never leave your back yard, so to speak. Trails like these, if purpose built for mountain biking, can be quite satisfying. There are many other examples in New England, like the recently built Russell Mill trails in Chelmsford, MA. When land space is limited, make the most of it. Perhaps the Isoperimetric Quotient shouldn't be applied here, and something more like a Fun-Factor makes more sense.  I probably wouldn't want to ride on dense trails like these every day, but once in a while can be quite a blast.

I've left out a class of routes that cross over themselves or momentarily touch in the middle. Sometimes this is unavoidable in some areas when putting a long ride together. Nothing wrong with that. You can still encircle lots of terrain in multiple lobes. In your training, make your miles count. If you want to go 20 miles, find a loop that makes many small angle turns, approximating something like a circle. Pick a route that puts the largest number of acres in the middle. You'll feel like you did more, went somewhere, accomplished something. Doing the same training rides throughout the year can get boring enough. Seeing the same thing twice in a single workout doubles the boredom factor.