# How to calculate forces for most appropriate electric engine for soft sand? [duplicate]

I'm super new to this topic I'm posting here so please forgive the nursery question and content. I'm hoping to use any answers to help me begin my research and investigation on what I need to learn.

I've been looking around the interwebs on how to calculate what size electric engine I need to move this garden cart on the beach (https://www.gorillacarts.com.au/product-page/gorilla-carts-450kg-steel-mesh).

I'm not at all interested in speed. I just want max torque to achieve my goal.

As I understand the basics of it...

As mentioned. I'm new to all this so probably slow on the uptake. I'm wanting to understand what big factors do I need to consider if I want to move this cart through soft beach sand. What measurements should I be taking and how do I convert that data to then select an appropriate engine?

I've seen similar questions posted on here on how to calculate forces for most appropriate engine but I'm not sure how wanting to operate on soft beach sand changes the math and approach.

I bought a crane scale and pulled the cart across a variety of surfaces while at max intended load.

Max weight + unit = 158kg

Flat cement = 3.5kg peak inital force to pull

Flat cement 10%'ish uphill grade = 14kg

Soft Flat sand = 41 kg

I realise there are a bunch of factors which will be difficult to measure i.e engine/bat inefficiencies but what are the big things I should be figuring out and how to translate that to the hardware requirements?

What the best tyre type for soft sand will play a big role I'm sure in engine choice. My values were on the stock wheels. I need to understand what would be the best tyres for soft sand.

Thanks very much for any help anyone can share with their knowledge and/or experience in the topic.

Thanks, Nick

• Tires? Check out dune buggies. Nov 14 '21 at 11:17
• "I'm not at all interested in speed" well you to specify something or the problem is not well posed. Would you be happy with 1 millimeter per month as the speed? If so then almost any motor at all will work. If not, then what is the minimum speed you can accept? Nov 14 '21 at 20:07
• The basic is what torque is required to overcome the friction force of the sand due to the weight of the cart, then the power required to produce the torque and the demand speed. There is a lot of factors that need to be considered, you need to read all the fundamentals of automotive engineering.
– r13
Nov 15 '21 at 14:43
• Duplicate: How can I calculate the power and torque required for the motor on a wheeled robot/vehicle? Soft sand: I would use a coefficient of rolling friction of at least 0.3, but probably 0.5, maybe even 0.7. Recommend 6 wheels or tracks because high ground pressure = sinking in = essentially going uphill all the time = higher coefficient of rolling friction. Even your giant 13" wheels will be unsatisfactory, I think. Nov 15 '21 at 14:45
• Observe your wheels in your sand pulling tests. Were the wheels skidding? Because coefficient of rolling friction of 41kg/158kg = 0.26 feels low to me for soft beach sand. Nov 15 '21 at 14:51

You have already measured some facts. You need continuous pulling force = the weight of 41 kg on the sand. That's the case when the vehicle has been already lifted up from the notches which will be formed under the tyres soon after the vehicle is stopped. You must know also the needed initial pull. It depends on how deep notches there already are below the tyres and what acceleration you expect. And you need these with full load.

The acceleration needs force (in Newtons) = total mass (kilograms) x the speed increasing rate (meters/second in one second). That's an extra which must be added to what's needed to pull up the tyres from the notches below them and to win the continuous sand resistance. To be exact some more is needed to accelerate the wheel rotation, but I guess the rotational inertia of the wheels is small when compared to the translational inertia of the whole system.

It's easiest to measure the total start force when pulling the van to move.

Then you must know how much forward pushing force your tyres can deliver. Lock the rear wheels (I guess they will be powered) and check what's the needed force to pull the vehicle - do it both with light an full load.

I'm afraid pulling as 2 wheels locked shows that you need rear tyres with deep paddles. You simply do not get the needed traction with the originals which probably are designed for low rolling resistance on hard surfaces.

In theory any motor could produce as much forward pushing force as wanted if there's a gearbox with high enough ratio. To have also some driving speed you need power. You can calculate it in 2 ways:

1. The power in watts = Driving speed (meters/s) x Pulling force (Newtons). Sorry for using SI units, but they make everything much less error prone.

2. The power in watts = Rotation speed of an axis (radians per second) x Torque (Newtonmeters).

The torque calculations are essential, as you probably knew. You can calculate the axis torque in Newtonmeters by multiplying the pulling force (=Newtons) with the radius of your powered wheel (=Meters).

You can change the driving speed to axis rotation speed by calculating how many revolutions of a wheel is needed per second for the wanted driving speed. Multiply it with 2Pi (=6.28) to get the result in radians per second or with 60 to get revolutions per minute. Gears multiply the rotation speed and divide the the axis torque with the same number, so gears do not affect the power (except by having friction, you need some reserve).

It's up to you to find a motor which can produce the needed torque for starting to move when stalled. Old fashioned DC motors (with brushes) are best in that sense. Modern electronically controlled brushless motors can be close. In addition the motor must output the needed torque for nominal driving speed at motor's nominal rotation speed continuously.

It's a challenge to keep water and sand out of the motor and to keep the motor cool enough. Designing the easy to use and reliable electricity system with all needed protections is another challenge. I guess you should search for existing solutions when the power, speed and torque requirements are calculated. Have at least 25% reserve.

Not asked, but do not even think that someone would sit in the van. It's already an unstable vehicle (high, narrow, no stabilization mechanisms) and a person + the safety cage would make it intolerable. It can work as a carriage where electricity only helps on the sand. The max speed you need is about 1,5 meters/second. To reach that speed in 0.5 seconds with full 158 kg (brt.) load you'll need acceleration force 474N (or about 48 kg as you may say). In addition you need what's needed to push the vehicle up from the notches and to win the sand resistance.