Is This Street too Narrow to Make a 3 Point Turn?

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Ksatterfield

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I know this is an odd topic but we just returned from the Department of Motor Vehicles and despite numerous attempts, we cannot get our car to successfully complete a three point turn on the narrow street that they have just started using on their route. Our car is a 2010 Volvo XC90 and it has a 20.5' turning radius. The street is about 17' wide. The dimensions of my car are: 189.3" long and 74.7" wide.

Is there a way mathematically to PROVE that this car cannot successfully make a legal three point turn on such a narrow road? What is the minimum width we would need for the street to be in order to successfully complete the three point turn?

FYI - Most lanes are 12' wide so a standard two lane road would be 24' wide. Those 7 feet make a big difference!!

Thanks for your help!
 
Here is a link that shows how to do it but at the end it says move back and forth until you are perpendicular. In order to do it legally, you have to complete the maneuver in only three moves. If you do the back and forth thing, you fail.

http://www.ehow.com/video_1870_make-three-point.html

Here is the written description:THE THREE POINT TURN

* 1. SIGNAL WITH YOUR RIGHT DIRECTIONAL. PULL OVER TO THE RIGHT AND STOP...... SIGNAL WITH YOUR LEFT SIGNAL AND CHECK FOR TRAFFIC.
* 2. WHEN CLEAR TURN LEFT CROSSING THE ROAD UNTILL YOU ARE FACING THE CURB.
* 3. CHECK AGAIN FOR TRAFFIC. TURN YOUR WHEELS AS FAR TO THE RIGHT AS THEY WILL GO AND BACK UP TO THE OPPOSITE CURB OF THE ROAD.
* 4. STOP, CHECK AGAIN FOR TRAFFIC AND PULL AWAY FROM THE CURB
 
A standard legal 3-point turn consists of this, assuming a right-side drive paragigm:
1) Approaching one direction in a legal lane.
2) Continuing forward, Turning as hard and as sharply as possible to the left, across the opposite lane until the roadway is exceeded.
3) Picking a reverse gear, turning as hard and as sharply as possible to the right, across the original lane until the roadway is exceeded.
4) Returning to a forward motion, turning as hard and as sharply as possible to the left, into the lane in the opposite direction as the original motion.

The hypotenuse must fit at each stopping point.

The ONLY restriction to eventual accomplishment, given level ground, is the hypotenuse.

189.3" / 12 = 15.8 '
74.7" / 12 = 6.3'

\(\displaystyle \sqrt{(15.8)^{2}+(6.3)^{2}}' = \sqrt{289.4}' = 17.0097'\)

Well, since that value is greater than 17' (Actually, exactly equal will do), you cannot do it in ANY number of points.

HOWEVER

There was quite a bit of rounding going on in there.

If we truncate, rather than round, we get.

189.3" / 12 = 15.7'
74.7" / 12 = 6.2'

\(\displaystyle \sqrt{(15.7)^{2}+(6.2)^{2}}' = \sqrt{289.4}' = 16.8798'\)

Theoretically, we could do it in SOME number of points.

For me, the fact that it is SO CLOSE to the limit proves that it essentailly cannot be done. 3 points? No way.

347 points? Maybe.
 
Ksatterfield said:
Here is the written description:THE THREE POINT TURN

* 1. SIGNAL WITH YOUR RIGHT DIRECTIONAL. PULL OVER TO THE RIGHT AND STOP...... SIGNAL WITH YOUR LEFT SIGNAL AND CHECK FOR TRAFFIC.
* 2. WHEN CLEAR TURN LEFT CROSSING THE ROAD UNTILL YOU ARE FACING THE CURB.
* 3. CHECK AGAIN FOR TRAFFIC. TURN YOUR WHEELS AS FAR TO THE RIGHT AS THEY WILL GO AND BACK UP TO THE OPPOSITE CURB OF THE ROAD.
* 4. STOP, CHECK AGAIN FOR TRAFFIC AND PULL AWAY FROM THE CURB
Click to expand...

Couple of oddities.

First, #2 is a little weird. Why would you stop when facing the curb. Most likely, one would continue as far as possible.

Second, depending on the situation, you may have more room than you think. If you are trying this between two solid structures, you are stuck with the external hypotenuse as described above. If there are low or no curbs and no guide rails, you probably will be able to use some fo the space under your vehicle to complete tha maneuver. I'd guess the wheel base plus one tire diameter would be a good estimate of the minimum eventually possible. Depending on the height of the curb, that could decrease a little.
 
Thank you so much for your reply. It is very helpful. The curb is low. The wheelbase is 112.6 and the tire diameter is 19". This car does not turn sharply at all. My last car had a very tight turning radius and this car does not. I have found two statistics for the turning radius of the 2010 Volvo XC90. One just lists turning radius as 20.5' and the other says curb to curb turning radius is 40'. It would seem curb to curb would apply here.

Would these stats still support the impossible in three moves theory? Thank you again for your help. This is all way over my head.

Kristina
 
This vehicle, in 17 feet? No way if we define "to the curb" as the exterior limits of the vehicle and not the tires.

I tried to draw some pretty pictures, but I'm not that good an artist and they were horrible.
 
Thanks again for your help. Does turning radius not matter at all since there is no curb? A car the same size with a smaller turning radius would do fine. Correct?
 
If the diagonals don't fit (Sorry, I've been calling them "the hypotenuse"), turning radius will not matter at all. If it CAN be done at all, then turning radius will make it happen in a smaller space or in fewer attampts.
 
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