Here is some better info on mormon handcarts.
http://en.wikipedia.org/wiki/Mormon_handcart_pioneers
It will tell you the numbers. A large majority made it. The two companies that left late and encountered tragedy still had a high survival rate. There are a few things the handcarts taught us. First is the speed. They were faster than wagons pulled by animals. It took a week or two for the people to get in shape, but once they got used to pulling the carts, people walked faster than the horses. Yes, they carried less weight, but in companies that had a mix of handcarts and wagons, the handcarts would go ahead and then have to stop early so the wagons could catch up. The same was true with the children. After a few weeks of walking every day, the children got used to it, and would walk ahead, and then play for hours waiting for their parents to catch up.
Of course, now we live in a modern world. We can use that to our advantage with making a cart. The first is bearings. Make sure the wheels you use have good bearings. That will increase your efficiency and amount of weight you can carry. Also, rubber wheels. You don't even need pneumatic tires. You can buy tubes that are filled with foam that never get flat. I would look at either BMX tires or mountain bike tires. I think BMX tires are 21 inches, and mountain bike tires are 26, at least the standard sizes. Road tires have less drag on the road, but have no floatation in sand. Using modern materials to build the frame will really help, of course. 2 wheels is more maneuverable than 4, and has less drag. But, it can't hold as much weight. You also have to balance the weight correctly to not put too much stress on the yoke. If you do 3 wheels, I would put the castor in the back, it is easier to pull it through sand than push it. Good luck.
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