landscapingoutdoorrope-knots
I have an old walnut tree that I want to attach a knotted rope to for my boys to climb. Would the rope in the pic be a good choice? I am looking for something that would not hurt their hands too much and would be able to withstand some inclement weather.
Sorry, I can't help you with the type of grass. But I do have some suggestions that will work with any type.
Don't just leave it dirt. Improve the dirt. Add compost to the soil. If necessary, have the compost roto-tilled in.
Organic matter helps the soil to retain moisture. Periodically aerate the soil (yearly is a good idea if you can do so. A pull-behind aerator is not that expensive if you have a small tractor, and well worth the expense.) After each aeration, add more compost on the surface. Grass with a deep, robust root system can survive a period of no water for longer than otherwise.
You may also find it a good idea to check your soil for problems. Is it heavy clay? Sand? Are there problem trees in the area, like walnut? Is the soil too acidic?
4" of packed gravel (tamped every 2" with a plate vibrator) will meet all your requirements: cost, DIY and drainage. In fact, unless you are sited over clay, no slope will be needed: rain will percolate through.
If you want a more formal surface, add an inch of sand and top with pavers or flagstone.
Use a mix of crushed 3/4 gravel with fines (particles all the way down to stone dust, 21AA in my area)
Plate vibrator: 
Best Answer
IMHO that's much too small in diameter for comfort. Possibly also for safety in that material. The "safe working load" listed is almost certainly not one involving using the rope for supporting people or things above people, where it's typical to derate (or over-size) by a factor of 7 or more.
IMPE a 1 inch/25mm to 1.5 inch/37mm diameter rope is more typical for a "knotted climbing rope" in manila. That may be sold as 3 - 4.5 inch (circumference) rope depending how it's listed for sale.
I'm dubious of sisal for the job as it's somewhat more prickly (the major use I'm familiar with it from is as haybale twine - and that's hard on the hands.)
Plastic or plastic blend ropes will hold up to weather better than natural fibers, but can be damaged by sun over time.