IsambardKBrunel
Posts: 12
Joined: 4/3/2013
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This is probably not what you're looking for, but there's a physics-based incentive as to why.
The same reason why we wear seatbelts and have airbags in cars is most likely the same reason a large, wide paddle will hurt more than a flimsy (in comparison) cane or a strap.
That reason is Delta T, or change in time.
Delta T is important in an impact, because with the same amount of force impacting the object, the longer it takes for that object to impact you, the less damage you'll cause since that force is being spread out over a longer period of time.
When you get into an accident, there are three impacts. First, the mean nasty object in your way hits your car. Second, your body in some way impacts the car. Third, your internal organs hit your ribcage. It's usually the third one that kills people, but since we can't put padding there to increase Delta T, we put (comparatively) elastic seatbelts and fluffy cushioned airbags to prolong that Delta T and expend that energy over longer periods of time.
Still with me? Alright. So as you can imagine, straps are pretty elastic. The force carried through them will bleed off once it hits you, because it's wobbling all over the place. Since most of the force bounces off you instead of a dead smack-and-stop, it doesn't transmit as much force onto your toushy. It acts as a seatbelt carrying its own force and lays into your butt over a longer period of time, and even expends some of its energy getting away from you on the rebound.
Canes don't have much surface area, and your skin (especially more cushioned areas) is pretty malleable. I'm sure if you looked at a high-speed camera of you being whipped, you'd see your skin mould around the cane like if you took a baseball bat to a water balloon. From the time of impact to the time of deepest penetration (dirty) and the time it takes to reverberate lengthens that very important Delta T. Also the cane will be bending, which eats up lots of force.
A paddle, however, has way too much surface area for your skin to mould around it. It also will not reverberate backwards because of this. From the time of impact to the time of dead-stop is SO much shorter than the other two, and that force has much more of an impact on your poor butt.
So there you have it: a winded, rambling answer from a bored Dom mechanical engineer.
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Either put it on your limits list, suffer or find someone who builds up your levels in baby steps so maybe you can get to a point where you not only tolerate it but excuse your dominant of hitting like a girl. <--always a mistake by the way and that's regardless of gender! 
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