Pulse and Glide - Average Speed
19/06/08 07:16 Filed in: Physics
Sometimes it takes an article to inspire me. I just
read an article about Dale Earnhardt Jr using
pulse-and-glide techniques in NASCAR and it
got me to thinking. The basic idea of pulse and
glide (as I understand it) is to not use your
engine as much when it is at a low load because
it is not as efficient. Instead, accelerate to
10 mph over your desired speed and coast to 10
mph under your speed limit. Apparently, this can
save fuel.
Here is the question: How do you drive to make your average desired speed?
Here is the question: How do you drive to make your average desired speed?
Suppose you drive such that your speed is like this:
This would obviously give you an average speed of 50 mph. Here you are increasing your speed for 2 minutes and then coasting for 2 minutes. Note that the the following graph would be unrealistic:
The biggest problem is the infinite accelerations going from 60 mph to 40 mph and back from 40 to 60. Well, perhaps this is just a very high acceleration. Then this would really defeat the goal of pulse and glide as you would be using your brakes to slow down and that would just be a dumb way to lose energy.
What if you did the following:
Hey its the same as before! No, its not. In this graph, you increase your speed from 40 mph to 50 mph over 2 miles, not two minutes. You then decrease your speed for 2 miles. It turns out this does NOT give an average speed of 50 mph.
Clearly, we are talking about one dimensional motion here (and by we, I mean me). So, I will use the following:
Suppose I drive 60 mph for 2
miles and then 40 mph for 2 miles (which is not
what the above graph says (it has non-constant
speeds - but I will proceed anyway). My average
speed is NOT 50 mph. Why? Let me do this the
long way. My average speed is my change in
position over my change in time.
Here, I know x1 and x2 (the distance traveled at each speed, but I do not explicitly know the times. I can find the times using:
Substituting these in for the times:
In this case, x1 = x2 so:
So, if the driver drives 60 mph then 40 mph for the same DISTANCE, then the average speed would be:
Great, you may say - but that doesn’t apply to pulse and glide, as you (I) stated above. Anyway, who would drive by watching the mileage markers instead of the clock?
Nonetheless, the same idea applies to second graph with regards to distance.
Really, I am just using this pulse and glide to talk about average velocity - see, I tricked you. But I think I would like to explore this pulse and glide technique a little more. I am confused on how this saves energy significantly. If you just drive slower, it seems that would be better (less energy loss to air resistance). It seems the claim is that the car engine is more efficient while speeding up than it is maintaining speed. This seems odd, but I am not too familiar with the efficiency characteristics of the car engine.
Hopefully I will return to this topic.
This would obviously give you an average speed of 50 mph. Here you are increasing your speed for 2 minutes and then coasting for 2 minutes. Note that the the following graph would be unrealistic:
The biggest problem is the infinite accelerations going from 60 mph to 40 mph and back from 40 to 60. Well, perhaps this is just a very high acceleration. Then this would really defeat the goal of pulse and glide as you would be using your brakes to slow down and that would just be a dumb way to lose energy.
What if you did the following:
Hey its the same as before! No, its not. In this graph, you increase your speed from 40 mph to 50 mph over 2 miles, not two minutes. You then decrease your speed for 2 miles. It turns out this does NOT give an average speed of 50 mph.
Clearly, we are talking about one dimensional motion here (and by we, I mean me). So, I will use the following:
Suppose I drive 60 mph for 2
miles and then 40 mph for 2 miles (which is not
what the above graph says (it has non-constant
speeds - but I will proceed anyway). My average
speed is NOT 50 mph. Why? Let me do this the
long way. My average speed is my change in
position over my change in time.
Here, I know x1 and x2 (the distance traveled at each speed, but I do not explicitly know the times. I can find the times using:
Substituting these in for the times:
In this case, x1 = x2 so:
So, if the driver drives 60 mph then 40 mph for the same DISTANCE, then the average speed would be:
Great, you may say - but that doesn’t apply to pulse and glide, as you (I) stated above. Anyway, who would drive by watching the mileage markers instead of the clock?
Nonetheless, the same idea applies to second graph with regards to distance.
Really, I am just using this pulse and glide to talk about average velocity - see, I tricked you. But I think I would like to explore this pulse and glide technique a little more. I am confused on how this saves energy significantly. If you just drive slower, it seems that would be better (less energy loss to air resistance). It seems the claim is that the car engine is more efficient while speeding up than it is maintaining speed. This seems odd, but I am not too familiar with the efficiency characteristics of the car engine.
Hopefully I will return to this topic.
