Speed-Flow relationshio

[winner9459]

I came across the following Question and kind of depressed that I couldn't solve the problem. It appears to be easy

Problem 5: Transportation [E0304210006] 
For a four-lane freeway with a 60 mph design speed and an average travel speed of 45 mph, what is the expected maximum flow rate (pcphpl)?

1400 pcphp

l
2100 pcphpl


1700 pcphpl


2800 pcphpl

The answer given is as follows:

For a freeway, the maximum free flow rate (without traffic jam) is 2000 passenger cars per hour per lane (pcphpl), and according to HCM2000 Exhibit 13-2, using the average travel speed of 45 mph, the expected maximum flow rate estimated to be 2100 pcphpl.

My doubts are as follows:

1) Isn't the maximum free flow rate 2400, I also know that it is capacity flow rate, but how can I arrive at the 2000 pcphpl.

2) How the heck did the solution arrive at 2100 pcphpl. Using exhibit 13-2, it is not possible to determine flow rate with one known quantity.

Any help would be appreicated.

Thanks.

 

[winner9459]

OK guys, from my rudimentary understanding this is the conclusion I arrived at:

From exhibit 13-2 in HCM, we can see that speed will reduce starting at 1300 pcphpl, which is marked by a point on the curve, the points are successively marked for lower speeds of 65, 60, 55 mph also. I can notice that there is a increase of 150 pcphpl for each 5 mph increase in speed. Therefore by extrapolation, for 45 mph there should be an increase of 300 pcphpl for the 10 mph increase from the 55 mph speed, which results in 1750+300, i.e 2050, which is then rounded off to 2100 pcphpl.

This is totally a guess by me, if by any chance this is right, where can I verify and read about it ?

Also, I believe that the point at which the curves end in the exhibit represents capacity.......is that also true ?

Please correct me if I am wrong.

 

[Ambrug20]

OK guys, from my rudimentary understanding this is the conclusion I arrived at:
From exhibit 13-2 in HCM, we can see that speed will reduce starting at 1300 pcphpl, which is marked by a point on the curve, the points are successively marked for lower speeds of 65, 60, 55 mph also. I can notice that there is a increase of 150 pcphpl for each 5 mph increase in speed. Therefore by extrapolation, for 45 mph there should be an increase of 300 pcphpl for the 10 mph increase from the 55 mph speed, which results in 1750+300, i.e 2050, which is then rounded off to 2100 pcphpl.

This is totally a guess by me, if by any chance this is right, where can I verify and read about it ?

Also, I believe that the point at which the curves end in the exhibit represents capacity.......is that also true ?

Please correct me if I am wrong.

well, I was thinking about this problem for a while. All i could do, is just a mark in my book that FFS=2000 for the speed of 45mph. i agree that it almost not possible to figure the data, based on this table.

 

[winner9459]

That sounds like a good idea, (I guess you meant V=2050 instead of FFS=2000, so the future readers wont be confused) of marking the maximum flow rate without any jam on the curves in the book before going to the exam.

 

[lady_j]

winner - I agree with you. The problem doesn't provide enough info to apply any type of formula, so this indicates that tables must be used.

I noticed the same trend as you did; that there is increase of aprox 150 pc/h/ln per every 5 mile decrease in average passenger car speed.

If anyone knows of another way to solve this, or can see an error in this analysis I'd love to know!

Thanks winner for posting. This gave me a mild anxiety attack as well....but its good to know what we might be facing!

 

[Ambrug20]

winner - I agree with you. The problem doesn't provide enough info to apply any type of formula, so this indicates that tables must be used.
I noticed the same trend as you did; that there is increase of aprox 150 pc/h/ln per every 5 mile decrease in average passenger car speed.

If anyone knows of another way to solve this, or can see an error in this analysis I'd love to know!

Thanks winner for posting. This gave me a mild anxiety attack as well....but its good to know what we might be facing!

if you can find the NOTE under the table 23-3 in HCM, it gaves the speed and capacity respectively, so you can make an assumption for speed 45mph. This is the best I could think of