Turning Radius of a Car

The post makes no sense at all.
Is it a statement or a question?
Either way, I don't think the terminology is correct.
AFIK the "turning radius" is determined by the steering geometry.

The maximum turning radius is infinity for all vehicles. (e.g running in a straight line)
maybe you mean minimum turning radius? And if you are talking about banked track, then it's probably correlates to the length of the vehicle and wheelbase!
Del

Maximum turn radius was never mentioned in above post. But my reading is off as well as my spelling.

Cant teach the English English!

Odd I miss read it, (I thought it was in the title) but it hardly makes any difference to my post.
Del
You can have a gold star in your work book (damn teacher's pet)

I take the gold star and you get a GA with a reservation against the maximum!

"But for a unbanked turn with following parameters known : wheelbase , track lenght , weight , front to rear weight distribution ratio , velocity of vehicle while making a turn and Center of gravity height from ground . "

It appears to me that the OP is asking what the minimum turning radius will be to initiate a change of direction in the vehicle when traveling in a straight line at a known rate of speed and taking into consideration all highlighted parameters/variables.

I don't think the OP knows what he is asking.

I've been there and I still go there every once in a while whether I want to or not.

Hopefully some of us can get him back on track and headed down the right path before he over-steers causing his turning radius to exceed his ability to maintain control and sanity.

It occurs to me that it is time for semester finals and I am sure glad I'm not going through that right now as I don't think I could handle it physically or mentally.

We need to make sure the young ones succeed otherwise we're going to be expected to bat cleanup and I can hardly see the ball much less make good solid contact with it at this point in life.

But as Comment #8 points out, he has NOT accounted for the coefficient of friction, i.e or in this case resistance to scrubbing [is that the right term?] during the turn. If he has assumed this is irrelevant -- a "spherical cow" problem -- he can go right to assuming the vehicle has no overhang and right to a solution; velocity is in that case not needed. I suspect he will need to account for friction and needs more information.

I didn't think much about Del's answer until you critiqued it for us.

I went back and read it again, and added another GA to his Tally.

Read the post again, allow for English not being the persons first language, or for a typo (that used "." instead of "?" and see/read,

"How to calculate minimum turn radius considering the above parameters"

- and then tell me how anyone with half a brain cannot reasonably interprete the post as a question and just a statement in the context of what this site is about ?

- yes this is off topic, but where else would it go.

Whatever became of the simple physics of banking the turn to fit the radius of the turn, so that the car's G vector is normal to the pavement, instead of attempting to produce axial slippage?

I tend to agree with Del, the minimum turn radius, is more related to the mechanical setup for steering the wheels (whether front or back or both), now the corner speed of an automobile, not completely like the corner speed of an aircraft is related to several factors, including lift, thrust, control surface (tires in the case of the car), and drag, as well as ambient conditions (for the airplane this includes local air density at the altitude in question, and also the temperature (as it affects density)). There is probably something I left out. It is purely a vector problem seeking an easy solution.

And to think Lewis Hamilton does this calculation in milliseconds by the seat of his pants at every bend in the F1 track.

This thread is not about the turning radius of a car, as that is a function of the activities of the driver, the design of the car, its speed, the nature of the surface, the condition of the tyres and the design minimum turning radius.

• See keywords "doughnuts and drifting" on YouTube.

For considerations of force, then for a Standard gauge rail vehicle, the equilibrium cant (the height the outer rail must be lifted above the inner rail for optimum passenger comfort) is:

• H=0.0562 V²/R, where H is the cant in inches, V the maximum line speed in miles per hour, and R the radius of the curve in chains.

However, common practice is to put on only 2/3 of that figure out of respect for vehicles travelling lower than line speed and the wear that takes place at the rails, which is excessive at optimum cant and tolerable at reduced cant. The mass of the vehicle is irrelevant. Does that help?

I'm not so sure the mass can be ignored. I recall from many years back, a fellow member of our electrical association, working for a tyre manufacturer, chatted about testing care tyres for grip and wear and tear, saying the driver had to turn a circle at maximum speed to cause skidding, then do his best to hold the skidding speed for the duration of the test. Tyre wear was measured.

It seems the outside tyres wore out faster because the weight of the car caused it to tilt, thus transferring the weight to the outer tyres which increased the grip to hold the circle - and the wear. Whereas the inner tyres had little weight and less wear.

This makes sense because in perfect conditions a skilled drive could get the car to lift and balance on the outer tyres only. In fact, this is a popular circus stunt where the car then can be driven in a straight line once balanced.

...bot OT, I thought cars lost their drive power because the diff box would cause the lifted tyre to spin in free air.....

The point here I am making here is the mass does have to be taken into account at some stage.

I take issue with " tightest circle that the vehicle can manage irrespective of speed".

I believe that turning radius is, " tightest circle that the vehicle can manage" which would be at its slowest speed.

At least at a speed of 0 the calculation is easy! - JHF

Do you want the wheels rolling or sliding over the pavement?

Which axis will the car turn around. I guess you want to keep it on its wheels.

Try to search for "Steering geometry" as Del suggested.

I can see this turning around very quick.

You'll find that once you introduce the coefficient of friction the weight/mass of the vehicle will cancel out in subsequent calculations.

Draw some force vectors. Sum of all forces = 0 and sum of all couples = 0.

The centripetal force will be acting on the center of mass, which you can find fore-aft from the weight distribution ratio and given height, and its magnitude is m*v^2/r.

Your minimum radius (or maximum centripetal force) will occur when:

1) the car rolls (downward force on inner tires <=0)

2) front or rear tires loose traction (horizontal force > vertical force x coefficient of friction)

The opposing forces will be supplied by the tires. The maximum horizontal tire forces will each be equal to the downward force x coefficient of friction. The downward force will be weight plus the couple due to the height of the center of gravity.

Find your tire forces as a function of the centripetal force. Find the centripetal force that corresponds to the minimum breaking point and work backwards.

Del was right, this this question or statement makes no sense.

There is no Centripetal Force involved in the turning radius of a car.

The car turns because someone turns the front wheels of the vehicle. The forces that cause the car to turn are transmitted thru the structure of the vehicle and interacts with the friction on the surface on which the car is turning.

The axis of rotation has no effect on the turning of the vehicle. Therefore no Centripetal Forces whatsoever.

True, but you have to read past the words and try to understand what he wants to know... how sharply can the car turn at a given speed, and how can you calculate that.

Fair enough.

The OP should understand that Centripetal forces are Orthogonal to axis of rotation.

In order for that to happen all four tires would have to be angled at the same degree and even then the forces felt inside the vehicle would be the result of the car turning, not the cause of it.

Time for the OP to stay awake in class and not mix up principles of physics and dynamics.

Agreed. There's clearly a relationship between turning radius, mass of vehicle, height of CoG, tyre coefficient of friction etc. If this the OP's project he should put in some mental effort and come up with something, using what he has presumably been taught.

Your "question" is so poorly worded that it is almost impossible to understand. Let's hope you do a better job on your thesis.

You need to start with researching vehicle dynamics. You are so far off with your factors and variables that it's almost a long distance call between reality and your perception of it.

I can only assume you are talking about maximum skid pad G load. I would give serious thought to looking at auto racing and race car design. The number of factors that determine maximum cornering potential are given a critical eye here since the vehicles are designed to cull out as much performance as humanly possible.

That means all of the factors are such as static and dynamic friction, aerodynamics, tire contact area, temperature, vehicle weight distribution, vehicle mass, and a host of other variables are considered in the final equations.

There should be plenty of scholarly papers on the subject to draw from. You might try contacting auto manufacturing companies. Introduce yourself as a student with a thesis and see if they have department that can help you. Getting your data from unknown forums is a recipe for a failing grade, if I were your instructor.

A synonym is celerity; a simpler word is speed. In physics, velocityspecifically refers to the measurement of the rate and direction of change in position of an object.there is a difference between "speed" and "velocity"

You can't with just those parameters. Design of the tires is needed. A lot to work with there. As the tread width. Durameter of the rubber. How well the steel bands give and move. Thread design. All factor in.

I guess it depends on who's driving...

Any vehicle will turn within the tightest radius at slow or slowest speeds which greatly minimises the variables and hence calculations.

Yes you can get the car to spin at higher speeds by sliding the back out to assist in the turn but the higher speeds will result in a larger turn radius extended in the direction of travel of the vehicle.

The math is also a lot more complex but can be calculated if that is your intention (for comparisons perhaps if the point is a purely mathematical exercise, which this may very well be being a college project where perhaps turn radius needs to be calculated at DIFFERENT speeds).

Well he doesn't mention max angle of wheel, which is restricted....I mean if you could turn the wheel 90° then your turning radius would be the center point of back wheels to the center point of front wheels times 2...for example a 2014 Mitsubishi Lancer Sedan has a wheelbase of 103.7 inches and a turning radius of 32.8 feet.....3.8 times it's wheelbase...2014 chevy sonic 34.5 feet turning radius with 99.4 inch wheelbase ...4.2 times it's wheelbase...I'm thinking somewhere between 33° to 53°....average maybe 40°....

It's not all that clear, but I don't think he's asking about steering geometry, but about the relation between radius of curve (not necessarily minimum radius) and vehicle speed, CoG height etc etc.

But why do the work for him? As Lyn often points out, it's not doing him any favours longterm.

Once he's shown how to do it maybe next time he'll know....isn't that what teaching is?

I believe that you give the OP far too much credit.

Learning how to define the problem has to enter into the process before learning can begin.

You can only impart, (teach), so much. Then it's up to the student to pick up the tools and use them. Assuming the OP is a male by gender, he claims to be in College and he seems to have a grasp on the math required to formulate the answers to his questions, if in fact they are questions? And, if in fact he is in college, he should invest the time in doing the physical experiments to prove his equations using scaled down models. That could be his first lesson in the school of hard knocks, right or wrong, thats the best teacher.

Yes but if this is his project he's presumably on some sort of engineering course and has been taught some first principles. He should apply them, or if he hasn't grasped them speak to his tutor.

That's only part 1 of the problem. Friction is not the only limiting factor; there is also overturning moment, in which case the car rolls rather than skids.

Wheelbase and front-rear weight distribution are minor players compared to track width, tire friction, and skid-vs-roll regime.

Don't forget to factor in the friction caused by back seat drivers.

I am sure this factor has been the root-cause of many over and under steering accidents.

This brings up a good point, the friction from the tires is going to vary according to tire characteristics and road surface characteristics which are constantly changing...the road surface changes with moisture, material of construction, age, wear characteristics...then the control systems built into today's vehicles also come into play, traction control, active suspension and others...there is no definitive friction amount except in real time....

I am dumbfounded by this thread.

Divine intervention is your only hope.

In the real world, if you're talking about speeds over - ooh, let's say 30mph - you have to consider aerodynamic forces.

This is by no means a technical analysis, but may give you some pointers:

http://www.rapid-racer.com/aerodynamic-upgrades.php

Google will yield much more information, with a bit of intelligent searching.

This smells bad. I think this is more homework.

The minimum turning radius on ice may be quite large.

Tyre Tear Out at Low Temperatures

I am not impressed many of the responses to your question - your wording may not be perfect, but the implications were clear enough.

It is homework so I will not hand you the answer on a plate - there are two or three main issues you need to think about.

What it the tightest turn or the minimum radius (steady state) the vehicle can do without sliding, and what physical values effects the result in this regard.

The (simple) answer is: velocity, radius and tyre friction because the mass effects cancel out - on one condition.

That one condition I refer to is another issue - "will the vehicle slide or tip first".

The (simple) factors that effect vehicle tipping that are vehicle width, or more correctly track width, the height of the centre of mass and the side force due to cornering. Once again, the mass effects cancel out.

You use moments to work out what is tipping the vehicle and what is stopping it from not tipping - and clearly the side force issue is common to both the speed/radius issue and the tipping issue, so there will be some sort of simultaneous equation. Either the tipping condition or sliding condition will likely occur first.

The above is a simplification of the real world because in the real world tyres distort and their effective coefficient of friction changes with load, temperature, tyre construction and tyre pressure.

There are also dynamic suspension effects which cause the load distribution between the front and rear axles to change, so that while in your simple world the axles share the mass and side forces in a way that causes both axles/tyre to slip at the same time, in the real world this may not be the case.

Tipping in the real world is also more complicated because tyres distort under load so the effective support point is inboard of the outer edge somewhere, the centre of mass of the vehicle usually moves across of the vehicle as it corners ((usually to the outside because the c of g of the vehicle is usually above the roll centre), as well as moving forward and backward a minute amount. (a second order effect arising out of the slope of the roll axis front to rear not being horizontal)

The reason I included "steady state" at the beginning of all this, is because the forces to cause a vehicle from moving from "straight ahead" to being "in the corner" have to accelerate the vehicles angular speed and increase its angular momentum from zero to whatever the figure is, steady state in the turn.

Now you might understand why few people actually know much about vehicle handling - and how hard your question could be if it was answered professionally.

Good luck with your project.

What about the ground? Differences in pavement type will create coherent answers. For instance a summer performance tire will do wonders on warm dry concrete, however that tire is terrible on cold wet slippery surfaces. The exact opposite is true for winter tires.

TrevorM #36. I was not aware that the OP wanted an answer that had to impress you. Sorry I will try harder next time.

But I certainly appreciate the effort you have put into your detailed explanation because it fills in a couple of forgotten gaps in my trip down Memory Lane, and also to SolarEagle #27 for adding some recognisable landmarks to help me find my way.

The OP has posed a question - that to us - is missing some important details -that has been pointed out. In reality the question could be answered by making (inventing) some assumptions. But still in reality, an insight to the science of the subject is needed to be aware that some parameters are missing - and their likely magnitude.

I appreciate the mass cancels out in the maths, but the way the statement is made, could give the OP the impression that mass can therefore be ignored.

This is not so. The mass is basic to the construction of the question and is needed to arrive at the answer(s).

Some posters are getting a bit carried away on this IMHO. Apart from it being undesirable to do OP's project for him (as opposed to offering a few hints), he hasn't been heard of since. If he has lost interest there's even less reason for the forum to work on it!

I am not in disagreement with you in principal but I have my own reasons for taking part.

I see this an informal chat room and whilst there is a protocol of good practice the that we try to observe I am not aware of rules of debate that says we must not give answers to project questions or expect the OP to reply.

It would be nice for the OP to respond with answers to our questions and to say thanks but that is just good manners. We are not bound to participate. We all have the choice of abandoning the OP. But we don't. Sometimes the question itself takes on a life if it own and the OP becomes forgotten. As has happened here (it seems) because to be honest, until you said, I had not noticed the OP had not responded.

For myself I help where I can. I give serious answers where I can, or flippant or cynical answers sometimes (hopefully readers can tell the difference) and always objectively where possible, but never offensively or in bad manners.

Where, from contributions by others; I learn something - which for most part is often from the discussion that wanders OT - the banter - the riposte - none of which would be possible if everything ran to strict rules.

That for me, is the fun of CR4.

There are far too many variables and unknowns to solve this one. That's the reason why it took some two decades for GM to design a chassis that is on par with BMW.

I may be off topic, but I think this will change minute by minute. Several decades ago, when drag racing was just getting started, someone tried to calculate the max speed a car could reach in a 1/4 mile. They came up with about 175 MPH. A Gentleman from Florida by the name of Garlits did not seem to agree and many others have backed him up since. JHF (This is an acceleration calculation isn't it?)

That works out to 0.77g. In theory friction can't exceed the down force, so that would be reasonable. But that was when drag racing was just getting started, I believe nowadays acceleration well over g is possible, using "sticky" tyres or something, no doubt leaving some of the rubber on the road.

Cover sheet for your project.

Afraid I don't see the connection ...

I remember this from (land) Surveying 1A & 1B classes back in the early seventies. They were taught by a Division of Highways Engineer on Saturday mornings, (back in the day...).

Wheeled-vehicles ''track'' such un-banked (flat) curves as portions of spirals with up to a 65 miles-per-hour design velocity, and thus, are only approximated as circular curves. Back in those days, with Highway Engineering, such curves were approximated by circular portions between straight-line tapers (ie: the actual circular portion of a 90 degree turn would, thusly, only have a central angle of 75 to 85 degrees between the two tapers, ala Hickerson, etc.)

Even so, wheeled vehicles tended to slide off the roadways in wet and/or icey conditions, unless such 90 degree turns were (banked) (ie: had their outside edges ''super-elevated'' some 3 to 6 percent, typically.) Otherwise, the velocity contributed to a vehicle's centrifugal force had to be counter-acted by the centripetal force of the driver trying to turn the steering wheel enough to stay (between-the-ditches).

In those days, highway engineers had experience-based tables (ie: Highway Engineering Design Manuals) to guide them in their roadway geometry design efforts. Actual calculation of spirals was too tedious to make all the necessary calculations to accommodate actual wheel-tracking, let alone easy to actually be laid-out by survey construction efforts (ie: Transits and Levels) of that era, in a very cost-effective manner. Nowadays, thanks to electronic calculators, surveying instruments, etc., such spiral portions should be much more easily calculated and constructed (does anybody else remember the ''Curta" ?)

Off course, some speedway race courses do have actually circular curves, but others look like giant rectangles with VERY rounded corners, when viewed from high enough overhead.

Highway Engineering and/or Traffic Engineering textbooks and/or Handbooks could be valuable references on such topics as the OP has mentioned...

First things first,

- What exactly is your ''project''?

- What sort of a class is it for? (ie: Math, Physics, Engineering, other?)

- Is it a solo project, or a group project? for a week, month, year, or longer?

- Is it a project for a single class, or a (Senior/Capstone) project, or just a single take-home kind of assignment?

- Is it to be a research type of project where you do some sort of measurements, testing, prototyping, etc., or is it a ''paper-only'' to be written/presented for review, or just turned-in for a single grade?

- What is your major course of study, and what role is this project to play in pursuit of that major?

- What were the relevant prerequisites for taking your class?

- What other relevant information can you provide?

I suggest that conduct some direct experiments, most likely in an empty sporting arena parking lot, and measure the radius diameter at minimum speed. There is your answer for your particular vehicle (which model number you should include in your homework answer. Now try the experiment going faster and faster, and see where all that smoke gets you. Once you have succeeded in rolling the car numerous times, thereby breaking your neck, it can safely be assumed that this homework will no longer be relevant.

By the way, be sure and drive safely, and wear your seat belt.

Also make sure that each car has some kind of approved roll cage (and wear a helmet) if you're taking the empirical approach.

Broken necks suck.