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Converting golf push cart to be rideable electric cart

I currently have 2, 24volt, 10.5 ah lithium ion batteries. What I want is for cart to be able to go top speed of 18 mph but would go about 12 mph on average. I just want to make sure it can handle going up hills in grass any steep hills I would just walk behind )and not go below 12 mph. I would like distance range to be 10 miles. If I can use the batteries I have great if not will buy correct ones for application. Total weight of me, cart and golf bag will be between 230 and 250 pounds. It will have 12 inch wheels. I need help with what set up I need. I am thinking I may need two motors because I would like to make it remote control also. Vary the speed of motors to make it turn. Is possible to make motors direct drive into wheels or will I have use gears and chain? Was hoping to get total list of parts with shematic. Then I would buy parts from electric scooter parts.com. Building the mechanical part I am fine with, it just making sure all the electrical components are compatible and capable for what I am trying to do. Thank you for any input.

To make sure that a motor or set of motors and the powertrain's gear ratio between the motor and the wheels can handle going up a steep hill we have a motor power calculator available on this page: https://electricscooterparts.com/motor-power-calculator.html

Once the top speed that can be used is determined then we have a top speed and gear ratio calculator for determining sprocket sizes on this page: https://electricscooterparts.com/motorwheelgearratio.html

Gear motors that wheels attach directly to are only available for slower speeds and they are not available for the speeds that you are designing the cart for so a chain and sprockets powertrain would need to be used. 

Once the required motor or motors power rating is calculated then we can make a kit out of the parts in which all of the parts will be electrically plug-and-play with each other. Making a schematic is time-consuming and not necessary if we make a kit, however, if you prefer to wire the parts together yourself from a schematic then we can create a schematic for you at a reasonable cost. 

A kit is definitely what I prefer. I'll take a look At links you provided and see if I can come up with something. I just don't want to guess. thanks
I punched in 500 watt brushless motor, 200 lb rider/cargo weight, 60 lbs vehicle weight, came out 19.98 mph on flat ground and 6.19 mph on 12% grade. Then punched in 2500, 14 teeth motor sprocket, 65 teeth wheel sprocket. 12 inch wheel height. Came out 19.3 mph. 4.64:1 ratio. If I could get setup for 2 motor set up and a 1 motor setup? Thanks

If the grade is intermittent and only for a few seconds such as a steep driveway then you could probably get away with a gear ratio for twice the 6.19 MPH 12% grade speed, however, if the grade is continuous such as going up it for 30 seconds or more then I recommend gearing for the 6.19 MPH 12% grade speed, or using a larger motor for a faster 12% grade speed. 

The smallest brushless motors that we carry are 48 Volts 1600 Watts so you could probably get the top speed and hill climbing ability that you want with one of them. 

I punched 1600 watt brushless motor, 200 lbs rider/cargo, 60lbs cart, it came out 31.91mph on flat ground and 17.46 mph on 12% grade. Then punched in 4800 rpm, 11 teeth on motor and 65 teeth on wheel 12 inch wheels, came out to be 29.09 mph and 5.91:1 ratio. ( I am assuming I am doing calculations right)There is one or two golf courses I play that have some pretty long hills. I'd probably caution to the more powerful side. I will only be going about 12 to 15 mph max plus I want the cart to be capable of going 10 mile distance on single charge, even though 18 holes of golf is generally about 5 miles. I am still debating on how I will also make it remote control. 2 motors and control turns with slowing one motor down, or actaute a separate small motor for steering front wheels.
Can you give me setup kit for either option?

If the top speed of the 1600 Watt motor is 17.46 MPH on a 12% grade and the cart will be used on a 12% grade then I would aim towards a gear ratio that provides a top speed of around 17 MPH. 

We have a 9 tooth sprocket for #25 chain (SPR-2509C) that fits the 1600 Watt brushless motor and we have an 89 tooth wheel sprocket for #25 chain. With this setup, the calculator is showing a top speed of 17.38 MPH.

We do not carry remote control parts so we are not able to build remote control functions into a kit, however, we could make a dual motor kit with two controllers if you would like to add a remote control throttle with skid steering. Or we could make a single motor kit with one controller if you want the remote control to steer the front wheels. The controllers have a +1 Volt DC through +4 Volt DC throttle input signal range. 

Please let us know your thoughts and we can take it from there.

I like the option of two Motors and two controllers. With the gear ratio set up that you suggested. Thank you.
Do you have set up?

My apologies for the late reply. I got a couple of weeks behind on forum replies and am just getting caught up today. 

I can make a kit out of everything that we have discussed. These 1600 Watt motors run on 48 Volts so the kit will need a 48 Volt battery pack.

Calculating the right battery pack size can be difficult on mixed terrain because the terrain could be mostly hills. mostly flat, or somewhere in between. As long as the terrain is not mostly hills then a 48 Volt 22Ah battery pack should have no problem with a 1-hour runtime. 

What are your thoughts on the battery pack?

Sounds good.
I agree with your battery choice. Do you have kit suggestion, with detailed parts list? Thank you

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