# Built on Facts

## Use the Force

#### July 30th, 2008 · 6 Comments

In daily life, there’s pretty much three kinds of frictional forces that you’re likely to encounter if you classify them by how much they are affected by speed. We’ll not worry about the direction of those forces since for our purposes it’s good enough to say that friction acts in the direction opposite the motion. So we can drop the vector notation.

The first one is those frictional forces not affected by speed, like sliding friction. As a good first approximation, this is given by

The frictional force is just equal to some constant depending of what material are producing the friction times the force perpendicular to the surface which your object is sliding across. Heavier objects mean more frictional force. It’s easier to slide a book across the floor than it is to slide a piano across the floor. But it really doesn’t matter how fast you do the pushing, the force per distance stays the same.

The second is viscous resistance. Dip a smooth stick into the still waters of a pond and very slowly and smoothly move it around. You’ll feel a force resisting the motion which is proportional to the speed of the stick.

Also very easy. You have some constant b which depends on the size and shape of the object and the properties of the liquid. You have the velocity. Multiply them together and you get the force.

Now why do you have to move the stick very slowly and smoothly? Because if you start moving it too quickly you’ll get turbulence. What’s turbulence? Basically, it’s lack of smoothness in the fluid flow. Like this picture, from Wikipedia:

Once you get turbulent flow, the frictional force starts to be proportional to the square of your velocity.

The constants are unimportant, the v2 is the issue. Go twice as fast, and you have to put in four times the work. While aerodynamic drag is definitely not the only thing sapping a car’s forward progress, at highway speeds it’s a very significant effect. A car traveling at a slightly over the limit speed of 75 mph will experience about 1.15 times the drag as a car traveling at the speed limit of 70 mph. While 60 mph is hair-tearingly slow compared to 75 mph, it reduces drag by better than a factor of 50%. Now you definitely shouldn’t drive unsafely slow, but even cutting your speed to 70 from whatever slightly-over speed you usually prefer can save you considerable gas at the cost of only a tiny bit of extra travel time.

Tags: Physical Concepts

### 6 responses so far ↓

• 1 Uncle Al // Jul 30, 2008 at 11:22 am

Cars are closely spaced on a flowing freeway. The whole line is drafting. Air resistance arguments are for isolated lumps in wind tunnels.

Engines have maximum efficiency rpm (above US speed limits for German-built cars - the Autobahn). California gas mileage is crunched by anti-pollution spaghetti under the hood that cuts out at high speed. Speed adds mpg faster than a small Cd car loses it.. Uncle Al’s 1989 VW Golf goes from 27 mpg nominal to 31 mpg doing sustained 90 mph to the Renaissance Faire with everybody else.

The El Toro Y is 26 lanes wide, flowing at 80 mph absent cops. A “fuel saving” 55 mph loses 31% of its throughput. What mileage improvement obtains when 400,000 cars/day do 8 mph? Anything government beneficently imposes will screw you. That is a Wreave bet.

• 2 CCPhysicist // Jul 30, 2008 at 6:06 pm

The other detail is that the drag coefficient is not a constant. It also depends on velocity, usually in a complicated fashion via the Reynolds Number.

Uncle Al forgets that you can put the car in any rpm band at any speed by choosing your gear accordingly. I recommend a series of controlled experiments.

He also forgets the risks of drafting, one of which will turn that Golf into a Ball.

• 3 Uncle Al // Jul 31, 2008 at 12:58 pm

Points taken, though weakened by discrete 3-speed trannies or doing 4000 rpm at 50 mph.. CCPhysicist has never driven from Santa Barbara to LA on a Sunday afternoon. Envision four lanes of horizon to horizon bumper-to-bumper traffic doing 70 mph. That is empirical fact.

The best way to improve gas mileage is to end speed limits and commuter lanes. Any flow trumps stop and go. Social activism imposes waste not, have not.

• 4 Chris P // Aug 1, 2008 at 12:20 pm

Hmm not a good start here.

Twice as fast means 4 times the drag. Work is drag times speed so work is up by a factor of 8.

Matt replies: Power is drag times speed. Work is drag times distance. Doubling the speed uses 8 times the power but only for 1/2 as long, so either way you slice it it’s 4 times the total energy used.

Why would there be any speed limits if one’s car used no fuel?

I don’t understand why I have to punished because people didn’t listen to the predictions that were made in the Club of Rome report “Limits to Growth” published way back in 1973. I always buy cars that get better mileage than the last one. Apparently some people don’t.

• 5 Lakeisha // Apr 17, 2011 at 8:03 am

jOuNFS Toucwhodn! That’s a really cool way of putting it!

• 6 Image // Jul 31, 2012 at 10:06 am

:D;):(;(:|:/:o:*:x:>8-):@;>:):p