Vehicle Speeds

[arithmetic anomaly]

Greetings. I apologize in advance for not following the typical forum etiquette and introducing myself, but I have a somewhat urgent question that I need help with. I keep getting different answers and at last I find myself on freemathhelp. Below is my summary and variables:

A vehicle collides with with a wall at 25 MPH, what was the initial speed of the vehicle before braking?

Vehicle Weight - 3100 Pounds
Vehicle Drag Coefficient - .35
Braking Efficiency - 1.00
Average Skid Distance - 66.5 Feet
Estimated Speed of Collision - 25 Miles Per Hour
Drag Factor of Road Surface - .50 OR .90

If someone could help me figure out an answer using .50 and .90 for Drag Factor I would greatly appreciate it. I also hate to ask, but could someone please explain how they came up with the answer? I would like to understand everything myself so I can use this for future math problems as well.

Thank You in advance for responding.

 

[Deleted member 4993]

Greetings. I apologize in advance for not following the typical forum etiquette and introducing myself, but I have a somewhat urgent question that I need help with. I keep getting different answers and at last I find myself on freemathhelp. Below is my summary and variables:

A vehicle collides with with a wall at 25 MPH, what was the initial speed of the vehicle before braking?

Vehicle Weight - 3100 Pounds
Vehicle Drag Coefficient - .35
Braking Efficiency - 1.00
Average Skid Distance - 66.5 Feet
Estimated Speed of Collision - 25 Miles Per Hour
Drag Factor of Road Surface - .50 OR .90

If someone could help me figure out an answer using .50 and .90 for Drag Factor I would greatly appreciate it. I also hate to ask, but could someone please explain how they came up with the answer? I would like to understand everything myself so I can use this for future math problems as well.

Thank You in advance for responding.

Since you keep getting different answers - you must have tried to solve the problem several times!

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[arithmetic anomaly]

My apologies. I have been using the equation S = 30 x D x F x N Squared

S = Speed, in miles per hour.
30 = A constant value used in this equation.
D = Skid Distance, in decimal feet and inches.
f = Drag factor for the road surface.
n = Braking efficiency as a percent.

Using .50 as Drag Factor I get 31.583
Using .90 as Drag Factor I get 42.373

But that equation only works if vehicle skidded and came to a complete stop. The vehicle in question skidded until it collided with a wall. The estimated speed of the vehicle after skid and before impact is 25MPH.

Also the equation I am using does not take into consideration the weight of vehicle or coefficient drag of the vehicle, and I have no idea what the 30=constant is either.

I do not actually need need the answer, just the equation and how to figure it out.

Thanks in advance.

 

[arithmetic anomaly]

I did not know if mattered the reasoning behind my questioning above, but maybe it will help explain my ignorance in regards to the actual math aspect of my question.

This is not an actual math question itself. I witnessed a collision and reported the car was driving too fast prior to colliding with the wall (rock formation). The officer then filed his report stating the car was only going 35 MPH before skidding and had slowed to 25 MPH apon impact, based on skid marks. The speed limit of the road is 35 MPH. My home owners association and I are trying to stop speeders in our neighborhood, because we all have children, and we are concerned for their safety. I can not say for certain the exact speed of the vehicle in question, but I am certain it was well above 35 MPH.

I figured someone who is more mathematically inclined could enlighten me. We are trying to petition to get the Collision Reconstruction Unit unit to come and view the accident markings, but I have a meeting with this districts captain tomorrow, and I would like some real numbers to show him, so I can persuade him to get someone else involved.

The officer originally stated he thought the car was going 45, because he was under the impression the speed limit of our road was 45. Once he was informed by one of our neighbors, that the speed limit was 35, he then stated the car must have been going 35. The driver of the car is the nephew of one our districts officers as well, so myself and our neighborhood believe some favoritism is in effect. This is why I am looking for some actual numbers, so I can show the captain that his officer may have been wrong, and it may need to be reviewed by more qualified individuals, outside of our district.

I have spent the last few hours researching car specifications and other numbers trying to figure out myself what the actual numbers could possibly be.

Again, thanks in advance.

 

[Deleted member 4993]

My apologies. I have been using the equation S = 30 x D x F x N Squared

S = Speed, in miles per hour.
30 = A constant value used in this equation.
D = Skid Distance, in decimal feet and inches.
f = Drag factor for the road surface.
n = Braking efficiency as a percent.

Using .50 as Drag Factor I get 31.583
Using .90 as Drag Factor I get 42.373

But that equation only works if vehicle skidded and came to a complete stop. The vehicle in question skidded until it collided with a wall. The estimated speed of the vehicle after skid and before impact is 25MPH.

Also the equation I am using does not take into consideration the weight of vehicle or coefficient drag of the vehicle, and I have no idea what the 30=constant is either.

I do not actually need need the answer, just the equation and how to figure it out.

Thanks in advance.

That equation looks wrong to me. There is a "square" relationship between initial speed and stopping distance - when the deceleration is constant.

Go to the following web-site for a calculator for speed and stopping distance for different road conditions:

http://forensicdynamics.com/stopping-distance-calculator

 

[Deleted member 4993]

Found the actual equation that you tried to use:

S² = 30 * D * f * n

Ref: Determining Vehicle Speeds From Skid Marks
by James O. Harris

 

[arithmetic anomaly]

That equation looks wrong to me. There is a "square" relationship between initial speed and stopping distance - when the deceleration is constant.

Go to the following web-site for a calculator for speed and stopping distance for different road conditions:

http://forensicdynamics.com/stopping-distance-calculator

Yes that site helps explain the actual stopping distance. But that only refers to a car that comes to a complete stop, not if the car collides with another object during the skid. The vehicle in question was still in the process of braking apon colliding with the wall.

 

[Deleted member 4993]

Yes that site helps explain the actual stopping distance. But that only refers to a car that comes to a complete stop, not if the car collides with another object during the skid. The vehicle in question was still in the process of braking apon colliding with the wall.

An estimate would be:

v² - u² = 30 * D * f * n

where:

v = initial speed (to be found)

u = final speed (25 mph here)

rest of the parameters have been defined before.

f	n	d	u	v
0.5	1	66.5	25	40.28027
0.9	1	66.5	25	49.19858

 

[arithmetic anomaly]

Wow. That makes total sense. So the estimated rate of speed would be somewhere between 40 and 50 MPH depending on the actual drag factor.

Do you know what the actual 30 constant means in this equation?

 

[stapel]

I witnessed a collision and reported the car was driving too fast prior to colliding with the wall (rock formation).... I can not say for certain the exact speed of the vehicle in question, but I am certain it was well above 35 MPH.

As far as I know, one would need way more information on the situation in order to do a proper modelling of the accident. The officer likely (in my experience) has a program on his on-board computer (or on some sort of pad) to do a rough model; the program contains various complex equations which are more likely to reflect "real world" accidents than might a simplistic "ideal" physics equation.

To get an accurate model, you might want to consider hiring a qualified forensic reconstructionist. But working just from skid marks will leave quite a lot of "wiggle room".