torque question

[donkey]

hey guys and girls, just a quick question about torque.
lets say I have a motorised device that total weight is 180KG(please use metric) if it was a 4wheeled device with top speed of about 5km and rear wheeled driven how much torque would I need to push the dang thing on a 45degree incline?
need info for a project not for homework (still haven't tried to get a qualification yet lol)

 

[Minder]

If there is a pulley or a sprocket on the driven shaft, use a empirical test using a spring scale and a cord is one method, or rig up some way of using a torque wrench.
Place it on the 45deg incline and obtain the reading that holds it stationary, if it is a size that makes it possible.
At 5km, the speed won't factor into it that much.
M.

 

[duke37]

My word, this goes back a few decades! I hope it is right.

Vertical force = 180 * 9.81 N (A kg is the basic unit, Gravity is 9.81m/s/s)
Force up the slope = 180 * 9.81 * cos45 = 927N (cos45 = 0.525)

The torque will be force * wheel radius(m)
Power will be speed (m/s) * force.
Edit
I think I was wrong, it should be sin45 = 0.851
So force = 180 * 9.81 * 0.851 = 1503N

 

[donkey]

So 1503 nm?
Just trying to figure out how much torque i need on a motor for a ride on device

 

[(*steve*)]

In real life things can get more complex.

At 45 degrees to need to ensure you don't lose grip.

If that power can hold you still, it won't get you moving.

If you're already moving and can trade speed for height, your kinetic energy can be traded for potential energy going up the slope, with the motor adding to it. This is otherwise called "getting a run up"

Your tyres will have a rolling resistance which will impart a need for extra power which can be considered linear with velocity. This grippy tyres you need to climb a 45 degree slot will have lots of rolling resistance.

At even higher speeds (you probably won't get here) you will need even higher power to maintain velocity due to air resistance. This is worse than linear and can be related to the square or even the cube of your speed.

 

[duke37]

So 1503 nm?
Just trying to figure out how much torque i need on a motor for a ride on device

Torque is force * wheel radius.
The torque would be 1503Nm if the wheel radius were 1m. Will you have wheels over six foot diameter?

The motor will be arranged to run fast with a lower torque by using a gear box. Remember that the gearbox will be inefficient, perhaps only 50% of the energy will get through.

Find out what power you need and then get a gearbox to match the torques. This will give the maximum speed.

 

[donkey]

well now you mention it a 2meter wheel would make the thing go REALLY fast.... and the neighbours would love to see it up and down the lawn lol
I was thinking go cart wheels so radius is about 10-15cm so will look at about 300nm ish? (that's the 1503nm described divided by 10 for 10 then multiplied by 2 for 50%efficiency) ... but that's still going to be fun to find and expensive I guess
also going off circumference 2pi*r at 15cm I get 94cm which is less than 1m so I need something over 5000rpm there too...... this is going to be SOO hard to find

 

[donkey]

I am hoping someone can tell me maths is way off up above because the highest torques I am finding are about 3nm

 

[donkey]

https://en.wikipedia.org/wiki/Tesla_Model_S#Specifications
I am thinking my maths is way off after reading that link. the car weighs 2 tonnes on average and needs 450nm torque. am assuming that 1/10th weight and smaller wheels will make it less

 

[donkey]

https://www.easycalculation.com/physics/classical-physics/force.php
So I used that calculator to get force
http://www.metric-conversions.org/speed/kilometers-per-hour-to-meters-per-second.htm
I used that calculator to turn 5km/h into 1.388889m/s

I knew weight was about 200kg
so the top calculator got me 276newtons
so on that 45 incline and going of dukes calculation I get newtons *cos gradient= 276*cos 45=195.16147160748711673463304394094

Lets round that sucker to 196 for fun

I know the radius of most go kart tyres are 10-15cm so 196 *0.15 =29.4nm IS MY MATHS RIGHT HERE???
I know the radius is 10-15cm so using circumference of 2 pi*r I get 0.94m I want speed to be 5km/h so that's 5000/0.94=5319.1489361702127659574468085106 or 5400for rounding IS MY MATHS RIGHT HERE???

 

[duke37]

In #3 I used cos at first and then edited it to the correct sin. This will make some difference to a figure with 30 places of accuracy.

A nm is a very, very small distance.
A Nm is a torque. Mr Newton likes his name to have a capital letter.

My calculation was to climb a 45 degree slope. As (*steve*) says, this is unrealistic. On the flat the torque necessary will be due to friction and the rate of acceleration.

For a speed of 5km/h, the SI value = 5000/60/60 = 1.4m/s
With a circumference of about 1m, this gives a rotational speed of 1.4 turns/second or 84rpm or 1.4 * 2 * pi = 8.8 radians/sec.

Power = force * speed, 1503 * 1.4 = 2.1 kilowatt to climb the slope.

Moderators
Why does the editor change k to K when writing 2kW? 2k1 is OK as is 5km.

 

[donkey]

isn't that 2.1nm?
I wanted something in NM and your maths seems to be same for both nm and kw
any chance I can get the equations to start figuring this out? I am getting horribly confused and would also like to learn lol

so your first one says to get torque or newton metres its force multiplied by wheel radius
so to calculate force I get m/s(metres per second) multiplied by weight in KG's
so that's (5000/60/60)=1.4m/s
1.4 * 0.15meters= 0.21watts but that sounds insanely small
also every calculator I use from Microsoft to web ones has sin45 at 0.707.....
all I want to do is calculate the torque of a motor needed to push my fat backside at about 5km.... having said that I now think closer to 300kg's might worth the look at as metal and batteries aren't light neither is the motor....

 

[donkey]

http://www.robotshop.com/blog/en/drive-motor-sizing-tool-9698
I went here and got the 2.1kw you gave I am just stumped on the maths

 

[donkey]

oh and I used 2 motors to get that btw

 

[donkey]

ok so I just looked at a disability scooter online and the motor they use is 400watt........ so will a 500watt motor work?
as Duke said it only has to be 84rpm, so most I see average 2500rpm... that has to be geared down by about 30 so torque or pushing power goes up by 30..... grrrrr. I am stumped... can someone point to an electric motor (2would be awesome) to make a ride on lawnmower please......... this is hurting my head now

 

[donkey]

evidence is stacking that this is possible now...... highly doubt that little scooter is a hoon mobile so would hope 2 500w 24vmotors can handle the job. (1each back tyre)

 

[duke37]

My new calculator was running in radians not degrees but my slide rule agrees with you at sin 45 = 0.707. I should have remembered this.
Gearing down the motor does not push up the power, it pushes up the torque or force and reduces the power somewhat due to losses.

With no friction losses, on the flat, the force is zero. Running on soft ground will need considerable energy.

The number of motors does not affect the calculations. Driving two wheels instead of one, gives more reliable traction on rough ground and each motor only needs to be half the size.

One of the links uses kgf for force, why complicate things when there is a proper SI unit.
Force = mass * acceleration
Torque = force * radius

Just remember that the basic unit for mass is not gram but kg.

There are suitable motors, controllers and batteries in mobility scooters, golf buggies and electric wheel chairs. You may be able to buy a cheap one if faulty.

 

[donkey]

So I see some of these disability scooters are 400watts so using two 500watt motors should get me close to where I want right?
also I am still at a loss on 2 things that someone has stated to me
1 500watts on 24volt is better than on 12volts.... I can't see why can you please enlighten me
2 AH I thought was the amps used per hour..... was told this is not exactly right... can I get more enlightened please

 

[(*steve*)]

500W is 500W. However, given that the batteries will weigh pretty much the same for the same capacity, a higher voltage means lower current and hence less weight in wiring (but this isn't going to be a huge issue).

Ah is a measure used to help describe the amount of energy in a battery. If multiplied by the voltage you get Wh, which are an actual measure of energy.

A Joule is a measure of energy

Watts are Joules per second (power -- the rate at which you use energy).

Wh are essentially power integrated over time, which is again just a measure of energy.

You get charged for electricity based on kWh, which is a measure of how much energy you've used, not how fast you've used it.

1 Wh = 1W for one hour = 1 Joule per second for 3600 seconds = 3600 Joules.

A 2Ah battery is one which can be fully discharged by a load drawing 100mA for 20 hours.

In general, Ah ratings are based on a 20 hour discharge. Due to resistive losses, a slower discharge will last slightly longer than expected and a faster discharge will not last as long as expected.

If you have a motor which requires 10A and you use a 5Ah battery, it will run something less than 30 minutes.

 

[donkey]

ok in regards to watts
lets say I have a 480watt motor (easier for my maths) If I have 2 150ah 12volt batteries. that's 3600 watt hours right?

so at 12 volt I get 7.5 hours which is the 3600 divide 480
at 24 volts I get 7.5 hours also
the only difference I see is that the amps and volts change