Caculating tractive force (i need a formula)

[dan_bighit]

i ve got the following question from my motor vechile diploma

kerbside weight 1360kg
rolling resistance 140N per 1000kg
frontal area 2m(squared)
drag coefficient 0.025

caculate the total tractive resistance when the car travels at 70 km/h on a level road?

what i need is the formula to work out tractive resistance I've searched for about 3 hours on the net but no luck.

any help appreciated

dan

 

[Hootenanny]

Firstly, ask yourself what is tractive resistance?

 

[dan_bighit]

is it traction

 

[Hootenanny]

is it traction

Which is what in terms of the forces acting on a vechicle?

 

[dan_bighit]

drag force

 

[Hootenanny]

drag force

Which would include the rolling resistance of the wheels and the fluid friction from the air, yes? So can you write down an equation for these two forces?

 

[dan_bighit]

i can work out the rolling resistance and air resistance which is
rolling resistnce = 190.4N
air resistance = 452.76N

what i need is a formula so i can caculate the total tractive force

 

[Hootenanny]

So, if the tractive force is the total or sum of all the drag forces acting on the vechicle, what do you think you should do now?

 

[dan_bighit]

add them together

 

[Hootenanny]

add them together

Sounds good to me

 

[dan_bighit]

ok here's the full question

kerbside weight 1360kg
rolling resistance 140N per 1000kg
frontal area 2m(squared)
drag coefficient 0.025

caculate the rolling resistance of the car?
caculate the gradient resistance when the car climbs a gradient of 1/20
caculate the air resistance of the car when it is traveling on a level road at 100 km/h?
caculate the total tractive resistance when the car travels at 70 km/h on a level road?

ive answered the top 3 questions but haven't used drag coeeficcient
and i thought that might come into tractive resistance but obvisily not. so where would that come into surly they couldent of just told you it for the sake of it.

 

[Hootenanny]

You should have used the drag coefficient in calculating the air resistance of the car.

 

[dan_bighit]

i got the formula formula form here http://www.webtec.co.uk/techinfo/equation/eqnfr/eqn01.htm

i think i see where I've gone wrong because I've worked out using 0.0462 when it should have been 0.025

if you could just clarfy this ill be happy thanks for your help

 

[Hootenanny]

My best guess is that you are required to use Stoke's-type formula to calculate the drag;

$$F = -bAv$$

where b is your drag coefficient. And we usually work in SI units, m, m/s², N etc.

 

[dan_bighit]

im abit confused now , what does the v mean.
so that formula on the website is wrong ?

 

[Hootenanny]

im abit confused now , what does the v mean.
so that formula on the website is wrong ?

v is the velocity or speed. No, the formula on that website is useful in some cases, but here you are given your own drag coefficient so you should use that. This formula is essentially the same as the one given on the website, with the exception of your own drag coefficient. Note, the correction in my previous post, the addition of cross sectional area A.

 

[dan_bighit]

is air resistance the same as drag resistance or are they diffrent?

 

[Hootenanny]

is air resistance the same as drag resistance or are they diffrent?

For your purposes they're exactly the same.

 

[dan_bighit]

so 0.025 x 19.444(m/s) = 0.4861 for stokes formula

0.0462 x 70^2(km/h) x 2 = 452.76N for the websites formula

these are 2 diffrent answers

thats where I am confused

 

[Hootenanny]

I really don't know where your getting your numbers from, don't forget the area in Stokes formula and that the website uses different units. What are the units of your drag coefficient.

 

[dan_bighit]

drag coefficiet units are k

 

[Hootenanny]

drag coefficiet units are k

and what might k stand for? Have you not been given any equation for calculating drag in your course?

 

[dan_bighit]

no its and extra course I am taking but, its all course work based, no classroom time. the only thing i can think of that k stands for is kilos.

 

[Hootenanny]

no its and extra course I am taking but, its all course work based, no classroom time. the only thing i can think of that k stands for is kilos.

No, that would be kg. In that case, I suggest you use my formula above;

$$F = -bAv$$

 

[dan_bighit]

so 0.025 x 2m^2 x 19.444 m/s = 1.944N

drag = 1.944 N

this doesent seem write

 

[Hootenanny]

so 0.025 x 2m^2 x 19.444 m/s = 1.944N

drag = 1.944 N

this doesent seem write

No it doesn't. Hmmm... its very difficult to do this without knowing the units of k.

 

[dan_bighit]

its all metric

heres the question again

kerbside weight 1360kg
rolling resistance 140N per 1000kg
frontal area (A) 2m^2
drag coefficient (k) 0.025

caculate the total tractive resistance when the car travels at 70 km/h on a level road?

so basically i need to caculate rolling resistance and air resistance and this will give the total tractive resistance.

which i got rolling resistance off 190.4N
using
RR = GVW x R /100
so i done 1360 x 14 / 100

now i need to work out air resistance (drag)

 

[Hootenanny]

Okay then, perhaps quadratic drag would be more appropriate;

$$F = -\frac{1}{2}k\rho A v^2$$

Where k, p, A and v are the drag coefficient, density of air, cross sectional area and velocity respectively. Do you have a model answer for this question?

 

[dan_bighit]

0.5 x 0.025 x 1.275 x 2 x 19.444 m/s^2 = 12.05N

does this seem write I am not to sure

thanks for your help

 

[Hootenanny]

I think I've found your problem. Your drag coefficient it way too low. 0.25 would be a more appropriate number, I think perhaps you question has a typo in it. There is no car I know of (engineers feel free to chip in here) with a k 0f 0.025.

 

[dan_bighit]

i think that's probably cracked it then

thanks

 

[Hootenanny]

i think that's probably cracked it then

thanks

No problem, I'm sorry it took so long! I can't believe it took me that long to spot it!