Mechanical Advantage for an Ebike Trailer

[EBikeTech]

Hello everyone! I am trying to figure out a work load / Pulling ability of trailers for the company I work for. We produce Electric bikes that have attachable utility trailers..

The general Wattage output for these E-bikes is 1000w. The trailers Mechanical advantage = 62.15MA. (WR=11 & AR= 4.5mm). But I am unsure how to further apply this formula to figure a capable weight the motors can pull / its Mechanical Advantage. Should I use the motors Torque or convert its watts to N m/s? Then converting this to usable Newtons has me stumped.

In layman's, I just want to learn the proper method or formula for calculating the motors ability to pull X weight on the units trailer.

Thank you so much for your time, as any guidance would be very valued.

 

[jrmichler]

You need a curve of motor torque vs motor RPM from the motor manufacturer. Then you choose a speed, and calculate the thrust from the motor torque, gear ratio, and wheel diameter. Then choose another speed and repeat. Continue, and plot the results, until you have a curve of available thrust vs speed.

Then you have to measure thrust required vs speed, required acceleration, weight, wind, and gradient. Take those measurement and compare each to the motor thrust vs speed curve. If the thrust required is less than thrust available, the motor will meet your needs at that point. If not, it won't.

 

[metastable]

@EBikeTech Can you please state the motor KV, motor resistance ohms, the battery voltage, the controller’s battery current limit, the tire diameter, the expected weight of the a) rider b) bicycle c) trailer d) load, and the slope in % you’d like to be able to climb, and the desired speed you’d like to maintain on this uphill slope?

 

[EBikeTech]

Hello! Thank you so much for the reply. I have no idea what the KV rating of the Motor is; as I never had to answer that. I just inquired some information from the manufacture to let me know the KV and Motor Ohm, along with a Torque curve sheet; I should have this info in the morning. The resistance is also problematic since its a 3 phase, and the only measurements I take of it are called a "Mosfet Test" and this usually just pretrains to the controller side of the motor.

The battery info I can gladly give you: We use a 48v (54v Full) pack using 18650 cells. The rating is 30 amperage on the packs BMS (but can jump up to 35 depending on load demand). The controller limit is 30a but will allow a slight over current. So 35a for just a few moments until the safety cut-off kicks in.

-The Tire Diameter is 22in (with tire installed).
- Rider weight: 180-240lb average customer base.
- Bike weight: 85lb
-Trailer weight: 30lbs
-Load is questionable as many customers use this for hunting. But trailer load average white tail deer; maybe 150-300lbs.
-Slope is dependent but at most, upwards of 10% grade.
- Sustained speed: anywhere from 5mph to 10mph.

If I receive that information in the morning I will attach it here. Thank you again for the help!

 

[Spinnor]

With the right gearing your motor could move a truck up a hill, very slowly. Can you change gears on the bike? Does the rider also pedal? What is the amp hour rating of your battery packs?

This system "smells" very underpowered.

How about an e-powered wheelbarrow or an e-powered cart and make the hunter walk?

From https://www.google.com/search?psb=1&tbm=shop&q=hunters deer cart&ved=0CAMQr4sDKAFqFwoTCKWAzau22-MCFVvw4wcdkq8OXxAC

The hunter should want the complete manly experience after he shoots the deer and have to put some effort into hauling back the kill?

 

[jrmichler]

If you want an E-bike that can pull a loaded trailer, you definitely need to run a test. A trailer carrying a dead deer is traveling over rough, soft ground. The rough ground has short, steep uphill grades, and the tires sink into the soft ground.

With the right gearing your motor could move a truck up a hill, very slowly. Can you change gears on the bike? Does the rider also pedal? What is the amp hour rating of your battery packs?

This. Very few deer hunters hunt more than a mile from their vehicles, so range and speed are not as important as pulling power.

If it will be used in the woods, a typical speed will be two to three MPH. At that speed, you no longer have an E-bike because the definition of E-bike is electric assisted pedaling. At the low speeds needed to travel through woods, the rider needs both feet out for stabilization, so cannot pedal.

 

[metastable]

Hello! Thank you so much for the reply. I have no idea what the KV rating of the Motor is; as I never had to answer that. I just inquired some information from the manufacture to let me know the KV and Motor Ohm, along with a Torque curve sheet; I should have this info in the morning. The resistance is also problematic since its a 3 phase, and the only measurements I take of it are called a "Mosfet Test" and this usually just pretrains to the controller side of the motor.
The battery info I can gladly give you: We use a 48v (54v Full) pack using 18650 cells. The rating is 30 amperage on the packs BMS (but can jump up to 35 depending on load demand). The controller limit is 30a but will allow a slight over current. So 35a for just a few moments until the safety cut-off kicks in.
-The Tire Diameter is 22in (with tire installed).
- Rider weight: 180-240lb average customer base.
- Bike weight: 85lb
-Trailer weight: 30lbs
-Load is questionable as many customers use this for hunting. But trailer load average white tail deer; maybe 150-300lbs.
-Slope is dependent but at most, upwards of 10% grade.
- Sustained speed: anywhere from 5mph to 10mph.

According to my calulations (& I'd be happy to share the formulas), on a 10 % slope with 655 $lbs$ total vehicle mass (297 $kg$), a 1 $meter$ frontal area, 0.75 drag coefficient, 9.80 $m/s^2$ gravity on earth, 1.23 $kg/m^3$ fluid density of air, (1) 30 $kv$ motor, with 0.05 $ohm$ resistance, 30 $amp$ battery current limit, 48 $volt$ battery voltage and 558 $mm$ diameter tires, the max possible velocity up slope is 10.4 $mph$ ( 4.65 $m/s$ ) assuming the optimal 8.76:1 turns motor:wheel gear ratio is used. If a different KV motor is chosen a different gear ratio will be necessary to achieve the max possible velocity. If the resistance is higher the top speed will be slightly lower (assuming optimal gear ratio is used) due to the increased copper losses. This assumes your drive wheel doesn't slip on the terrain.

 

[metastable]

 

[Spinnor]

That seems a bit optimistic. Power = mgh/t
m = 298kg
g = 9.8m/s^2
t = time
h = velocityxtimexgrade = 4.5m/s x time x 10% = .45m x time

power = 1300 watts

Given that the motor is 1000 watts you are pushing that bike a little too hard. On hard surface roads and at lower speeds bicycles are very efficient but once you get on rugged terrain or soft dirt roads efficiency goes way down. I know that biking on soft rails to trails bicycle paths really sucks your energy away. Best to bike on those trails when hard.

I Believe the above is rolling resistance for normal mountain bike plus rider, in the above case for roughly triple the weight you would roughly triple the numbers in the graph above?

Also, if the bike has only one gear it would have to be geared for the steepest and most rugged section of trail encountered slowing your progress down, easier than walking though. This is what I want to pull my dead deer cart with when I get an extra 5 grand or so,

Looks so fun might just skip hunting altogether. I know, for 5 grand you could get a pretty nice dirt bike.

 

[metastable]

That seems a bit optimistic. Power = mgh/t
m = 298kg
g = 9.8m/s^2
t = time
h = velocityxtimexgrade = 4.5m/s x time x 10% = .45m x time

power = 1300 watts

$48v * 30a = 1440w$ electrical power

$30a^2 * 0.05ohm = 45w$ copper loss

$1440w - 45w = 1395w$ peak mechanical power available...

then one has to factor the assumed $1m^2$ frontal area and $0.75$ coefficient of drag...

 

[metastable]

h = velocityxtimexgrade = 4.5m/s x time x 10%

shouldn’t this:

10%

be:

sin(atan(10/100))

 

[metastable]

Some of the electric “mountain boards” I’m familiar with have 4 motors (1 per wheel) each putting out 2.5kW, for a total of 10kW mechanical power for acceleration at full throttle — but I’m not sure how many dead deer carcasses someone could pull with one of those.

 

[EBikeTech]

@Spinnor The Units do utilize both a throttle and a PAS (Pedal Assist Sensor). They will over current for a short time, around 1,800w discharge but if sustained the BMS will cut the power to avoid damage. The units also use a mid-drive motor which will allow the motor to use the gearing on the back wheel to help with climbing or to increase speed.

Most customers don't come from a biking background so they think they can full power up a hill in the steepest gear ratio; but this always results in blown Mosfets on the controller side or melting phase wires and broken chains. The failure actually isn't cased by a over-current but the inability for the motor to turn properly which overheats the system (that's why we always say use the tallest gear when climbing any grade).

The customers have varying needs for distance; some only need to go a few miles on a fire road and others need to go 25 plus miles through rocky, ungroomed trails. The motor uses a 2:1 gear ratio and our better uses a 3:1 (which can handle up to 3,500w). I won't advertise our products here, but if you want to see a cool E-bike I recommend Luna Cycle based out of California. They have the best bang for your buck. Coming from a MTB racing background I adamantly try to get our owner to invest in better components and frame geometry; which respectfully he is willing to listen.

Luna Links: https://lunacycle.com/x-1-enduro-fs-ebike/
https://lunacycle.com/sur-ron-mx/

 

[jbriggs444]

sin(atan(10/100))

Small angle approximation. Try evaluating $\sin \tan^{-1} 0.1$