Ki Power - Dropping the Tanden in Aikido

Introduction

In Aikido the student is encouraged to drop his / her body a various times throughout just about every technique.  Why?  Physics can provide part of the answer by doing a calculation of the power generated.  The intention is for the dropped one-point to transfer energy to an aikidoka’s training partner (uke) in such a manner that they are projected or immobilized.  Equally this power can be transferred to a sword for a powerful (but relaxed) sword cut.

A look at how much power is generated by dropping the tanden just a few centimetres.  The results show that this is phenomenal power available to everyone that just bend their knees. Do this at precisely the right time and with uke stretched out and it is dynamic yet effortless.
Figure: Equivalent power you can generate just by dropping you knees a certain distance... its easy!!

The geeky stuff (tune out now if you want)

Key assumptions:

• Can accelerate the one-point to gravity (9.8m/S²)
• Entire body mass drops with one-point (not completely true since legs have a weight and are bending therefore not dropping at 1g)
• Power generated can be effectively transferred to uke.

Use Newton's laws of motion

• S = ut + ½ at2
• S = distance traveled
• U = initial velocity
• T = elapsed time
• A = acceleration (use gravity)
• Work = mgh (work done in raising an object to height h, also released)
• M = mass
• G = gravity
• H = height
• Power = W/t (Power generated is work done divided by the time it took)

Results

The Figure below shows the power generated as the one-point drops for a 50kg (110lb) and 100kg mass.  These would be equivalent to a 50kg and 90kg person I guess.  Note that after the one-point has dropped only 10cm over 1hp is generated by a 50kg mass.  This then continues to increase – but not as rapidly over distance.  Physics shows how much power can be generated but using it effectively is really the art of Aikido.  If we have 3 horsepower at our disposal but only move uke’s hand (because there is plenty of movement available in the elbow joint) it is wasted.  Only if the slack in uke is completely taken up can our 3 hp be effectively transferred resulting in projection of immobilization of uke.

Conclusion

Well it sure is a lot of power that the one point is generating. But if its only being generated for a short period of time the trick really is to use it effectively. i.e. if nage hasn’t got a connection to uke’s one point then all this power will be wasted in taking up the slack in uke's arms or something like that. Enter ikkyo, nikyo etc.. these techniques allow nage to tighten up uke so that all (or most of) the power generated by the one point is transmitted directly to uke’s one point.

Now if we are projecting uke then this power is effectively doubled by the ground because after being accelerated by the one-point they are then decelerated by the ground.

Appendix I – Matlab(C) code fragment from Figure 1

%calculate force, work and power over time of a dropping body %matlab code fragment body = 50; % weight of body gravity = 9.8; watts_to_horse = 1/764; s = [ 0:0.005:0.5]; t = sqrt(2*s/gravity); work = body*gravity*s; %use potential energy = mgh power = work./t; % power is work done over time inst_power = diff(work)./diff(t)*watts_to_horse; % look at work done in a particular time step plot(s(1:100),inst_power,s(1:100)+0.0025,inst_power*2); % look at instaneous power xlabel('Distance(m)'); ylabel('Horse power (hp)'); title ('Power generated through dropping of one point'); legend('50kg','100kg')