# Accelerating vehicles

• dondondon
Math is not your strong suit. You're trying to calculate how much gas would be saved if a roundabout was put in an intersection that currently has a stop sign. The power of the car is constant, so you can use Newton's law to calculate the velocity in terms of time. Since the time it takes to accelerate to 20 mph is the same for all cars, the amount of gas used is equal to the work done.f

#### dondondon

my community is debating the wisdom of putting a roundabout at a busy intersection.
we currently have a 4 way stop, and traffic backs up.
How much gas is used to accelerate your average 4000 lb vehicle from a dead stop ( as required by stop sign ) to 20 mph (apx speed to go through a roundabout)
I am trying to calculate how much gas would be saved

I think we need some differential equations here. Supposing that power of the car is constant, then driving force p/v then use Newton's law p/v-f=ma, assuming that friction is about constant. Then solve this equation to get velocity in terms of time.

Then get how much time is used to accelerate to 20 mph, work W=∫p dt=pt, since p is constant. I think here t can be expressed in terms of p and p would be canceled somewhere, then it depends only on friction f. You can experimentally determines how much friction is there. Work can then be used to calculate energy required and thus amount of gas via dividing by the efficiency of the car.

This is not an accurate model, since even ignoring air resistance, friction can be changing. But if there is no slipping, friction can be calculated in terms of angular velocity of the wheels thus the velocity of the car.

I am not very good at math. I don't know whether this is viable.

I am trying to calculate how much gas would be saved

That would be less to do with the dynamics of large bodies and more to do with the design of your lights. If you have long periods where you can anticipate shutting your motor off, and long amber lights, or some other early warning, then you can plan your approach and it will cost you next to no additional gas. If you have short light sequences and no early warning, then everyone gets frustrated and wears out their brakes/fuel money.

you are missing the point.. I just want to know how much energy (in gallons of gas ) is used to accelerate a 4 k lb vehicle from 0-20 mph

you are missing the point.. I just want to know how much energy (in gallons of gas ) is used to accelerate a 4 k lb vehicle from 0-20 mph

Have you considered my approach? Is it viable?

The energy used is equal to the work which is equal to the change in kinetic energy so the energy used to take a 4,000 lb object from rest to 20mph is 72,000 joules

you are missing the point.. I just want to know how much energy (in gallons of gas ) is used to accelerate a 4 k lb vehicle from 0-20 mph

You have to put in 0.5x9m/s^2x2000= ~80kJ.

Fuel has 32MJ per litre.

You'll not get much better than 25% conversion total from an engine doing a standing acceleration (my guess for some red-neck's petrol-powered 'utility vehicle') so you'll need 320kJ worth of that litre.. which is therefore around 10ml of fuel.

A roundabout is an archaec traffic methodology...we have lots in NJ and they work ok with light traffic...adequate vehicle separation...but with heavy traffic flow they become very inefficient...so NJ tends to provide bypasses for heavy flow traffic to avoid such roundabouts. They are excellent generators of traffic accidents, however.

thanks to all of you for your comments here. You have given me plenty to work with.
Also I grew up in N.J and had to run the "airport" circle near Philli almost every day (before they did the flyover.) This one is on Martha's Vineyard. Lots of debate about it. We currently have a 4 way stop there that really backs up in the summer. In winter, I hate the idea that every vehicle has to waste fuel by stopping. It drives me insane to see people leave their cars running while going into stores..
I like the site ,, Thanks again..
Don