From what I can tell anything below 5" or 6" (depending on context / techniques used) really won't make any difference in the range. It just means you don't have to hold the cain at the very end. Hand placement is always going to be about the same distance You'll either hold it towards the end for longer range or towards the middle. After 6" you start to get some extra space on the cane to use. In my opinion should be long enough to get some additional space where you hold the cane. There should be enough room on the straight end to hook wrists and elbows.
That little piece of the cane that is hooking around the arm is the extra space that you want. If you have to put your hands very close together to get that same amount then the cane is too short. The hand placement on the cane is about the distance you want to have in relation to the cane. This will give you to ability to use leverage, which is going to be vital in close range fighting with a cane.
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For me personally I rather have a cane that is the correct size for walking because at that point, the cane is longer than my longest weapon (my leg for kicking). The swing radius of a cane depends of the position of the hand. Holding the cane towards the middle shortens the range greatly. The range can be shorten or increased as needed so long as you can move your hand freely along the cane.
For example: the cane above is short range. He could easily swing in a restaurant space or sidewalk The swing range is a shorter distance than the elbow of the outstretch arm, But look at the picture blow. He has a nice range with room to spare. His arm isn't even extend so he's got plenty of long range available if needed.
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When fighting with a 6 foot staff the hand placement on a staff will determine the swing radius. This is also true for a cane.
The other thing you have to consider is the type of swing you are doing. You will run out of horizontal swing space before you run out of horizontal swing space. If I was in the same place as the guy in the middle, I could still do a vertical strike with a 6ft staff and not hit anyone else except the person I'm trying to hit. By you being short, you get an extra bonus in availability of vertical swing space. But in all reality. I'll probably gain some horizontal space after that initial swing. Most people are going to get up and get away from the guy with the swinging stick. Not many people want to become involved in such situations like that. You may have a couple of people who will try to tackle you, but most people don't want to be a part of the conflict that you have with the guy you are hitting.
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I'm 5'9" My sword in sheath is 39.5" which is a good size as it comes up a little above my hip. I would want a cane this size because I can place weight on it if needed. "36" is too small for walking and it feels too small when I use for a 2 hand swing of a cane that size. It's great for a two hand sword swing that requires both hands to be at the end, but it's horrible for swing where I need my hands to be far apart. Even a two hand thrust feels very short. But my sword in sheath feels just right for that vertical down strike followed by a thrust. using 2 hands.
It's going to ultimately boil down to which options you want to have available one hand options vs two hand options. I can swing a 39." cane like a one hand weapon, But I don't think I can use the "36" like a two hand weapon. This size only applies to me and my height. The size will be different for you.