Calculating maxium incline ablity.

[ericmark]

I am sure there is a formula, engine max torque, gear, transfer box, and axles ratios, and wheel size, one would need then to allow some leeway so maybe using the old 2πNT/33,000 to get the torque at max BHP which would be lower.

However the spec sheets seem to show speed at 1000 rpm, this should allow for tyre size, as saying it has 17" wheels does not help as that is not the tyre size.

So I suspect there will be a number x speed at 1000 RPM x BHP = pounds pull. Then some trigonometry formula that needs car + caravan weight and the pounds pull and will give you the incline that it will climb.

So if the result = 1 in 8 then I will know anything more than 1 in 10 needs avoiding. And if 1 in 2.5 then I can pull caravan up any UK road, as 1 in 3 is the steepest. 1 in 4 on a major road (Sutton Bank) and there are quite a few 1 in 6 hills.

I have used a 62 BHP car to tow a 14 foot caravan up Sutton bank, Curb car weight estimated: 1270 kg / 2800 lbs caravan around 14 cwt in third gear at 1000 rpm is would travel at 11.9 mph / 2.02 ratio of transfer box so 5.9 MPH at 1000 RPM I returned to pull another caravan stuck on the hill and only got into second low so 3.4 MPH at 1000 RPM, I started in first gear which would have given 2 MPH at 1000 RPM and I would not have liked to have started off in anything other than first low. Oh the car I used was 1962 Austin Gipsy.

The caravan I towed from standing start on the hill was being towed by a 1.3 Marina which got half way up first section, it was heavier than my caravan, no wonder he did not make it. However I am lead to under stand the towing weight is what the car can pull up a 1 in 12 which is really not that steep. So even with a permitted tow weight of 3000 kg and a caravan max weight of 1450 kg that does not mean I can pull it up any hill. I am likely to want to go through Much Wenlock and that is a 1 in 6 hill, so question is could I actually tow up that hill?

Again I have a car with a low ratio box, actually nearly the same final ratio as old Gipsy around 40 to 1, but more power around 168 BHP and diesel not petrol, wheel 17" not 16" but tyre profile means very similar however car and caravan weigh more.

So would like to be able to work it out before we try to climb any hills rather than after.

 

[bernardgreen]

Some clutch breaking ( and maybe record breaking ) steep hills in Wales

https://www.bbc.co.uk/news/uk-wales-45420155

 

[ericmark]

I don't expect there is a caravan site at the top, so not really worried about narrow country lanes, I think Sutton Bank (1 in 4) is about steepest A road, with a bend half way, but huge signs telling you well in advance, so unlikely to find it by accident. Much Wenlock however does not have massive signs with diversion shown for caravans, and that is 1 in 6 and that is steeper than what a car is designed to go up with maximum train weight being towed, I am not on my maximum however, the vehicle is rated at twice what I am towing.

I would not select a route with steep hills, hand brakes would pass at 25% not sure what that is, but one has to calculate that some one in front could get stuck, and you may need to hold car on the hand brake and then do a hill start when cleared. But I would still like to know my limit.

 

[Avocet]

I am sure there is a formula, engine max torque, gear, transfer box, and axles ratios, and wheel size, one would need then to allow some leeway so maybe using the old 2πNT/33,000 to get the torque at max BHP which would be lower.

However the spec sheets seem to show speed at 1000 rpm, this should allow for tyre size, as saying it has 17" wheels does not help as that is not the tyre size.

So I suspect there will be a number x speed at 1000 RPM x BHP = pounds pull. Then some trigonometry formula that needs car + caravan weight and the pounds pull and will give you the incline that it will climb.

So if the result = 1 in 8 then I will know anything more than 1 in 10 needs avoiding. And if 1 in 2.5 then I can pull caravan up any UK road, as 1 in 3 is the steepest. 1 in 4 on a major road (Sutton Bank) and there are quite a few 1 in 6 hills.

I have used a 62 BHP car to tow a 14 foot caravan up Sutton bank, Curb car weight estimated: 1270 kg / 2800 lbs caravan around 14 cwt in third gear at 1000 rpm is would travel at 11.9 mph / 2.02 ratio of transfer box so 5.9 MPH at 1000 RPM I returned to pull another caravan stuck on the hill and only got into second low so 3.4 MPH at 1000 RPM, I started in first gear which would have given 2 MPH at 1000 RPM and I would not have liked to have started off in anything other than first low. Oh the car I used was 1962 Austin Gipsy.

The caravan I towed from standing start on the hill was being towed by a 1.3 Marina which got half way up first section, it was heavier than my caravan, no wonder he did not make it. However I am lead to under stand the towing weight is what the car can pull up a 1 in 12 which is really not that steep. So even with a permitted tow weight of 3000 kg and a caravan max weight of 1450 kg that does not mean I can pull it up any hill. I am likely to want to go through Much Wenlock and that is a 1 in 6 hill, so question is could I actually tow up that hill?

Again I have a car with a low ratio box, actually nearly the same final ratio as old Gipsy around 40 to 1, but more power around 168 BHP and diesel not petrol, wheel 17" not 16" but tyre profile means very similar however car and caravan weigh more.

So would like to be able to work it out before we try to climb any hills rather than after.

I'm sure there is! You'll need all your gear ratios, your tyre size and the engine's peak torque. Power doesn't really come into it (other than the more power you have, the faster you'll be able to climb a given gradient. HOWEVER, the limiting factor isn't often that. More usually, it's what your clutch can handle as a hill start. It's one thing starting the climb on the move and maintaining progress, but if you have to stop and re-start, that's where it tends to go wrong (and is too hard to calculate unless you're a clutch manufacturer).

 

[bernardgreen]

I am sure there is a formula, engine max torque

If the ascent is in first gear all the way then a formula might predict the outcome.

Changing up a gear has to be done very quickly to minimise the loss of speed during the change of gear. If the speed falls too low the engine may stall when the higher gear is engaged.

 

[ericmark]

I seem to remember working out in first gear low range the overall ratio is some thing like 40:1 nearly the same as old Austin Gipsy but engine far more powerful 168 BHP instead of 68 BHP however also heavier, I have the feeling grip would be the real limiting factor, however with a light car we seem to go up Much Wenlock hill quite regular, there are two things I would like to know, one can I go up it with caravan, and two would I need to select low range at the bottom?

I am reasonably sure I could get up it, and if I was forced to stop then I can select low range for a hill start, however I can't select low range on the move, and would like a run at the hill if possible. It is a long way around the hill, but if there is any question then would prefer to go around than take a chance. It is a 1:6 hill on a major road, the tow car is a Kia Sorento, maximum permitted towing weight is 3000 kg and maximum loaded weight of caravan is 1450 kg.

 

[Burnerman]

You'd probably get there in low ratio so long as you didn't have to stop......restarting would largely depend on the state of the clutch.
John

 

[Avocet]

I seem to remember working out in first gear low range the overall ratio is some thing like 40:1 nearly the same as old Austin Gipsy but engine far more powerful 168 BHP instead of 68 BHP however also heavier, I have the feeling grip would be the real limiting factor, however with a light car we seem to go up Much Wenlock hill quite regular, there are two things I would like to know, one can I go up it with caravan, and two would I need to select low range at the bottom?

I am reasonably sure I could get up it, and if I was forced to stop then I can select low range for a hill start, however I can't select low range on the move, and would like a run at the hill if possible. It is a long way around the hill, but if there is any question then would prefer to go around than take a chance. It is a 1:6 hill on a major road, the tow car is a Kia Sorento, maximum permitted towing weight is 3000 kg and maximum loaded weight of caravan is 1450 kg.

OK, any idea what peak torque is? Also, the various gear ratios and tyre size.

 

[ericmark]

Overall gear ratio 40:1 that's first gear low ratio,
tyre size well 16 inch rim.
Torque net:
392 Nm / 289 ft-lb

Power curves, the power band is between 2000 and 3800 rpm, maximum torque at 2000 maximum power 3800 so torque using 2 pi NT/33000 = 252 ft/pounds at 3800 and 298 ft/pounds at 2000 rpm (given) so looking at gear ratio 40:1 easy enough to work out torque at the four wheels, but rolling circumference I have to date been stumped with, however data says speed at 1000 rpm is 5.3 mph in first so divide by 2.48 transfer box ratio = 2.24 mph at 1000 rpm so want 2000 rpm so 4.27 mph (375.76 feet per minute) at maximum torque.

Gear ratios (overall):
I 4.393 (16.39) x 2.48 = 40.6472
II 2.306 (8.6) x 2.48 =21.328
III 1.452 (5.42) x 2.48 =13.4416
IV 1 (3.73) x 2.48 =9.2504
V 0.825 (3.08) x 2.48 =7.6384

So 298 ft/lbs x 40.6472 gear ratio x 2000 rpm / 375.76 feet per minute = 64471.29 pounds pull car is 4387 unladen and 5820 laden so some where I have got it wrong. Hence the question. It would seem pointless to have a vehicle which can drive its self up a vertical wall, for one thing it would have no grip.

 

[Avocet]

Overall gear ratio 40:1 that's first gear low ratio,
tyre size well 16 inch rim.
Torque net:
392 Nm / 289 ft-lb

Power curves, the power band is between 2000 and 3800 rpm, maximum torque at 2000 maximum power 3800 so torque using 2 pi NT/33000 = 252 ft/pounds at 3800 and 298 ft/pounds at 2000 rpm (given) so looking at gear ratio 40:1 easy enough to work out torque at the four wheels, but rolling circumference I have to date been stumped with, however data says speed at 1000 rpm is 5.3 mph in first so divide by 2.48 transfer box ratio = 2.24 mph at 1000 rpm so want 2000 rpm so 4.27 mph (375.76 feet per minute) at maximum torque.

Gear ratios (overall):
I 4.393 (16.39) x 2.48 = 40.6472
II 2.306 (8.6) x 2.48 =21.328
III 1.452 (5.42) x 2.48 =13.4416
IV 1 (3.73) x 2.48 =9.2504
V 0.825 (3.08) x 2.48 =7.6384

So 298 ft/lbs x 40.6472 gear ratio x 2000 rpm / 375.76 feet per minute = 64471.29 pounds pull car is 4387 unladen and 5820 laden so some where I have got it wrong. Hence the question. It would seem pointless to have a vehicle which can drive its self up a vertical wall, for one thing it would have no grip.

OK. I'm away at the minute, and gave up trying to do this on my mobile phone screen! You're right taking the max torque and multiplying it by the overall gear reduction (40). That gives you the torque going down the driveshafts. You don't multiply it by 2000 because that is just the engine speed at which peak torque is available. (So for example, you wouldn't get twice as much if you were doing 4000 RPM). It means you get 298 at that speed and less at any other speed, that's all so you've already put the most torque you can get out of the engine into the equation.

So, 298 x 40. Then you need to DIVIDE by the tyre's rolling radius to get the tractive effort at the contact patch. If you search for "online tyre calculator", there are loads of sites that will give you the rolling radius (or even static laden radius will be close enough for this). If you're working in Imperial units, you'll need to convert the figure to feet. That will then give you the number of pounds of "push" that the tyre can give, assuming it doesn't slip.

 

[Keithmac]

Our Kuga is 163hp and 360nm iirc.

Never had a problem on any hill ( including Garrowby) with our 1550kg Sterling although the box us dual clutch auto.

As said above depends on the health of the clutch setting off from a standing start on a steep hill.

 

[Avocet]

Overall gear ratio 40:1 that's first gear low ratio,
tyre size well 16 inch rim.
Torque net:
392 Nm / 289 ft-lb

Power curves, the power band is between 2000 and 3800 rpm, maximum torque at 2000 maximum power 3800 so torque using 2 pi NT/33000 = 252 ft/pounds at 3800 and 298 ft/pounds at 2000 rpm (given) so looking at gear ratio 40:1 easy enough to work out torque at the four wheels, but rolling circumference I have to date been stumped with, however data says speed at 1000 rpm is 5.3 mph in first so divide by 2.48 transfer box ratio = 2.24 mph at 1000 rpm so want 2000 rpm so 4.27 mph (375.76 feet per minute) at maximum torque.

Gear ratios (overall):
I 4.393 (16.39) x 2.48 = 40.6472
II 2.306 (8.6) x 2.48 =21.328
III 1.452 (5.42) x 2.48 =13.4416
IV 1 (3.73) x 2.48 =9.2504
V 0.825 (3.08) x 2.48 =7.6384

So 298 ft/lbs x 40.6472 gear ratio x 2000 rpm / 375.76 feet per minute = 64471.29 pounds pull car is 4387 unladen and 5820 laden so some where I have got it wrong. Hence the question. It would seem pointless to have a vehicle which can drive its self up a vertical wall, for one thing it would have no grip.

If you give me the size off the tyre sidewall (e.g. 205 / 60 R 16) I can find a rolling radius for you, if that helps?

 

[ericmark]

There is a site called http://www.automobile-catalog.com/ this site gives gear ratios and power and torque for most cars, it also gives speed at 1000 RPM in each gear and car weight. My hope was to use the information given on that website to work out the theoretical incline each car could climb towing a set weight say 1300 kgs.

It also gives:-
Standard tire size: 245/70 R 16 H
Tire width (mm): 245
Tire sidewall factor: 70
Rim size (in): 16
Total wheel diameter (mm / in): 749 / 29.5

I am getting max pull 2235 kg and car weighs laden 2640 kg which would seem to show for that car limit is more to do with friction grip tyres to road than the cars power. However the 900 kg pull in high range is more interesting that seems to show max gradient of 1:4.4 if I have calculated correct, so the 1:6 hill would be on the edge in 1st High but would likely do it if I did not need to stop, and if I stop then clearly go into low range.

 

[motorbiking]

Are you concerning yourself with grip (friction), in your formula? Is the vehicle moving at the start? This makes a big difference.

Our Moho (front wheel drive 2.2l diesel 3.5 tonne with approx 140bhp/300nm used to need a bit of a run up to get up the ferry ramps, mostly because the weight would shift back and the ramps where metal. But on more than one occasion I was running out of grunt due to having to go slower than expected.

most cars will spin their wheels long before they run out of puff.

 

[Avocet]

OK, so we're assuming:

Max vehicle weight of 2640 kg
Max trailer weight of 1450 kg
Max torque of 392 Nm
Overall gear ratio (1st gear, low ratio and final drive ratio combined) of 40 :1
Tyre size of 245 / 70 16 (Which gives a diameter of 749mm and therefore a radius (give-or-take) of 375 mm).

I tried to check the gear ratios on that site you gave but there are loads of Kia Sorentos listed. I have no idea what model year or version yours is or whether it's manual, auto, etc! I DID have a quick look at one of them, but it didn't appear to quote any transfer box ratio. Also, it is confusing how it quotes "overall" gear ratio because you then don't know whether the final drive ratio is included in that figure or not. You're better off trying to get the data out of Kia UK.

The way you'd normally work out the torque supplied to the wheels would then be: Engine torque x 1st gear ratio (e.g. 4 :1) x transfer box ratio (e.g. 2:1) x final drive ratio (e.g. 5:1) So that would be 392 Nm x 4 x 2 x 5 = 15680 Nm as a torque applied to the wheels. (Which strikes me as surprisingly high)! That's obviously going to be shared between the 4 wheels (assuming it is 4 wheel drive, which I'm guessing it is because it has a set of low ratios)? It will be shared in whatever proportion the manufacturer has decided on the torque split - so it could be (say) 60% front and 40% rear). Anyway, for the purposes of this exercise, it doesn't really matter.

You then take that torque and divide it by the tyre radius (which is half the diameter, so it is 0.375 metres). That gives you a theoretical amount of "pull" at the tyre contact patch.

15680 / 0.375 = 41813 N (which is about 40 tonnes of pull)!

OK, you then need to knock a bit off for the losses in the drivetrain (it won't be 100% efficient. Let's say it is 80% efficient). That brings it down to 33450N You can get a more accurate idea if you can attach the car and caravan together on level ground (fully-laden) and try to pull them along using a big weighing scale. You want to get an idea of how hard you have to pull to make them start moving. That 3450N will be about 340 kg of "pull" - which is quite a lot. I doubt you'd need that much on the level).

You then need to knock off something for rolling resistance. Again, I'm guessing here, but let's assume 4 wheels on the car and 4 on the caravan and I'm going to take a wild guess and knock off 3450N for rolling resistance at low speed (because it makes the sums easier). That leaves us with a round 30,000 N to pull it up the hill. I'm not going to knock anything off for wind resistance because I'm assuming you're not going to be going very fast at 2000 RPM in first gear, low ratio!

The hill itself is easy. The force to drag something up a slope is the mass x gravity x the sine of the angle of the hill. If you say it's a 1 in 6, that works out at an angle of about 9.5 degrees. You have a total mass of 2640 + 1450 kg to pull up there, so the force needed to do it is going to be:

4090 x 9.81 x Sin 9.5 = 4090 x 9.81 x 0.1650 = 6622 N.

(So as you have 30,000 N available and you only need 6622N, it should be a breeze)!

HOWEVER, there are a load of caveats in this:

1. Check the gear ratios. They do seem VERY low!
2. Most hills are quoted as being a particular slope, but in reality, that's the AVERAGE slope from top to bottom. There will be parts of that hill that will be a bit steeper, I guess.
3. The calculation is based on being able to keep the engine at peak torque all the way up. If you have to lift off the throttle at any point (say for a cyclist or slower vehicle), you'll drop down the torque curve somewhat! You may be better getting the graph and giving me the figures for torque (say) 500 revs either side of peak torque.
4. You'll seriously annoy anyone else trying to get up the hill because you'll be going VERY slowly!! At 2000 revs, through a 40 :1 reduction, the wheels will be turning at 2000/40 RPM (50 RPM). The circumference of those tyres is 2 x Pi x 0.375 m which is 2.35 m. At 50 RPM of the wheels, you'll be covering 118 metres per minute or 7 km/h or 4.4 MPH!
5. As others have said, your tyres will be the limiting factor (unless you have to do a hill start, in which case, it might be your clutch)! If the road is wet, I'm going to guess at a coefficient of friction of about 0.7. Going up a slope, the weight will be light on the front wheels (let's say about 600kg on each one) so no matter how much "grunt" your engine can shove down the driveshafts, they'll start spinning if you ask them to provide a tractive force of more than about 4000N. That's each, so 8000N between them ASSUMING they each have the same amount of grip. THIS is where it will go pear-shaped because they never do, and unless you have a diff lock, the diff will just spin the easiest wheel, once it has lost traction. Of course, fully-laden, your rear wheels will have more grip. but we don't know about the centre diff on the Sorento. If it is an "open" diff, it will just send the torque to the front wheels as soon as they start spinning. If the Sorento is sophisticated enough to have traction control, then how much of the engine's torque gets to the tyres with the most grip, is anybody's guess!

The "bottom line" (based on the figures you've provided) is that in your low ratio you will have MORE THAN ENOUGH "grunt" but you're getting close to the front wheels starting to spin and you'll be moving VERY slowly! IF it was my car, I'd probably try this at night, in the dry, keep as much weight on the front wheels as possible, and if you're confident of not having to stop, maybe do it in a higher gear.