# How much does a gram matter?

disclaimer: I am going to use mixed units throughout this blog post. Get over it. I'll also be rounding a lot to the nearest order of magnitude.

I recently peeled all of the stickers off my mountain bike. They weighed in at 10 grams. My question is: how much does 10 grams matter on a bike? I realize the answer is going to be "not much," but it's fun for me to quantify these things.

We can start with a quick back of the envelope estimate assuming that my performance is directly proportional to my total weight: 10 grams is about 0.015% of my weight plus my bike weight:

$\frac{10 grams}{60 kg+10 kg}\approx 0.015\%$

We can go a little more in depth if we assume that the weight savings affects two main components of my ride: The weight I have to carry on climbs, and the reduced rolling resistance over my entire ride. I'll use a typical morning MTB ride as a case study. We'll say this is a 15 km ride with an elevation gain of 500 meters. My average power output is 100 Watts, for about an hour, resulting in a total effort of 100 Calories (kilocalories).

### Climbing weight:

Work equals Force times Distance ($W=Fd$) where the force in this case is $F=mg$. We can thus quantify the work I have to do to lift the extra 10 grams:

$W=(10[g])(9.81[m/s^2])(500[m]) = 0.012[Calories]$

### Rolling Resistance:

Again, the work done by rolling resistance is going to be the increase in Frictional force over the total distance of my ride. This website gives rolling resistance for many different tires; however, the values are given in watts and so we'll need to back-calculate the rolling resistance coefficient, $c_{rr}$, for our example.

A tire close to what I use has a rolling resistance listed as 30 watts. We can back-calculate the rolling resistance coefficient as:

$c_{rr}=Power[watts]*\frac{1}{speed [mph]}*\frac{1}{Weight [N]}$

Plugging in the test parameters:

$c_{rr}=30 [watts]*\frac{1}{18 [mph]}*\frac{1}{42.5[kg] 9.81[m/s^2]}\approx 0.01$

Now we can figure out how much this works against us:

$W=c_{rr} m g d$

$W=(0.01)(10[grams])(9.81[m/s^2])(15[km])\approx 0.003[Calories]$.

### Total

Either way we calculate it, it seems my 10 grams improves my performance by about 0.015% (about 0.015 Calories saved). Nothing to write home about, but it's a free gain and I think it makes the bike look better, so why not?

### Some discussion

Some "weight weenies" go to extreme lengths to save every gram on their bike weight. If you fit into that category of cyclist, and that enhances your enjoyment of riding, then who am I to judge? It's worth noting that many bike races are won by a fraction of a percent (In the 1964 Olympic cycling road race, the time difference between 1st place and 100th place was $\approx 0.001%$*), so if you're competitive you might as well take every boost you can get. Lets face it... I'm not even close to 100th place on any strava leaderboards.

If you're looking to save weight, this article has some nice suggestions to save 1 kg on a road bike for less than $700$. What's interesting is they break all decisions down to g/$, with the most cost-effective improvement being switching to ultralight tubes. At $\infty$ g/$, this is the easiest and best savings available.

It's also worth noting that weight isn't everything. Many changes you make to your bike will affect the feel of the ride, and the most important thing is to have fun! So just go out and ride!

*a time trial would be a more accurate way to measure individual performance boost, but the 1964 olympics illustrates one of the closests races in history. I realize that a 10 gram weight savings wouldn't have boosted the 100th place finisher to the podium.