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By Charles Rhodes, P. Eng., Ph.D.

**INTRODUCTION:**

The first turn of the kata Heian Shodan starts from a fully upright forward facing position and goes 90 degrees Counter ClockWise (CCW). The Fisher Method of executing this turn achieves a smaller vertical axis moment of inertia and hence a greater turning speed than the JKA Method. The Fisher Method also enables more energy in the follow-on technique. This web page includes a mathematical analysis that compares the elapsed time for execution of this turn via the Fisher Method to the elapsed time for execution of this turn via the JKA Method.

Both the Fisher Method of executing Heian Shodan and the JKA Method of executing Heian Shodan start from a nominal shizen-tai position with the heel spacing equal to the distance from shoulder joint to shoulder joint.

**HEIAN SHODAN FIRST TURN - FISHER METHOD:**

**INITIAL POSITION:**

In Fisher Shotokan the initial position is shizen-tai facing 12:00 o'clock with the heels at shoulder width but the outside edges of the feet pointing straight forward toward 12:00 o'clock. Both legs are straight but not locked. Tuck the ass in and the chin in to unify the body on a vertical axis and to minimize the body vertical axis moment of inertia. The arms dangle at the sides, not in front of the body. Note that the initial hand position and initial foot orientation are significantly different than the JKA initial hand position and initial foot orientation.

**INITIAL MOVEMENTS:**

Look left and simultaneously do a CM vertical drop together with a 90 degree vertical axis CCW rotation of the right leg about the ball of the right foot. The CM drop provides the energy required to fully load the right leg and right ankle. The left foot rotates 90 degrees CCW about the left heel and then as weight is removed from the left leg by right leg loading upper body angular momentum causes the left heel to slide toward 5:00 o'clock until natural leg spacing is achieved. Simultaneously execute a 90 degree CCW hip motion that positions the hips shoman toward 9:00 o'clock. While the body trunk rotates 90 degrees CCW the left elbow remains against the trunk and the left forearm moves upwards in a vertical plane that points towards 12:00 o'clock. The left fist closes and the left hand rises with the left palm facing the neck. Do not pull the left elbow back or allow the left elbow off the trunk as that will increase the vertical axis moment of inertia and slow the turn. As the trunk rotates the left arm bends upwards at the elbow. The right arm simultaneously reverse punches chudan or gedan toward 9:00 o'clock.

As the trunk rotation reaches 90 degrees the left hand that is in set-gedan block motion reverses direction by bouncing off the right arm near the right shoulder. There is no pause in this arm motion. At this time the hips are in shoman toward 9:00 o'clock, the right leg is bent and fully loaded, the right heel is on the ground and **the right foot points toward 9:00 o'clock**. The right arm is extended toward 9:00 o'clock in a reverse punch and the left fist is in set-block motion near the right shoulder. The left foot is on the ground but bears little weight and is wherever the left hip positions it. This set of movements must be complete by the end of the vertical drop. Do not step during the vertical drop.

**CONTINUING MOVEMENT OPTIONS:**

There is an option to retreat by straightening the left leg and relaxing the right leg to move the CM backwards toward 3:00 o'clock. There is an option to extend the left arm toward 9:00 o'clock in a vertical shuto and then bend the left elbow backwards to bring the left hand to the right ear, thus deflecting an opponent's jodan punch past the right ear.

**CONTINUING MOVEMENTS:**

The right heel presses into the ground and the right leg unloads to provide the force vector required to both support the entire body weight and move the CM horizontally toward 9:00 o'clock. The left leg momentarily bears no weight as it half steps toward 9:00 o'clock. There is a simultaneous 45 degree vertical axis lower body CW rotation about the right hip joint so that the hips go from shoman to hamni toward 9:00 o'clock. The angular momentum of this lower body vertical axis CW rotation about the right hip is cancelled by the left arm which performs a big vertical axis CCW gedan block/strike. The right fist pulls back to the right hip and the back muscles pull the shoulder blades together, actions which together reinforce the left hand gedan block/strike.

**FINAL MOVEMENTS:**

The favourable position of the right foot allows launching the next right leg full step-punch while smoothly accelerating the CM movement toward 9:00 o'clock over the left leg MFLP. To attain the required speed the CM must pass over the left toe while the right foot is still in contact with the ground.

**FINAL MOVEMENT OPTION:**

There is an option for a right hand reverse punch if the opponent does not move back in response to the gedan block/strike.

**HEIAN SHODAN FIRST TURN - JKA METHOD:**

**INITIAL POSITION:**

In JKA Shotokan the initial position is shizen-tai facing 12:00 o'clock with the heels at shoulder width and the outside edges of the feet pointing at 45 degrees to the main embusen axes. The left foot points toward 10:30 and the right foot points toward 1:30. Both legs are straight but not locked. The fists hang in front of the hips directly over the feet.

Heian Shodan, as originally described by Gitchin Funakoshi, had a larger initial heel spacing. However, the modern JKA uses the shoulder width heel spacing described by M. Nakayama.

Increasing the shizen-tai position initial heel spacing requires a greater ratio of leg strength to body weight to achieve the same power at the Midpoint Fully Loaded Position (MFLP) because the CM is further forward from the loaded leg.

**INITIAL MOVEMENTS:**

Look left and then do a Center of Mass (CM) vertical drop to load the muscles of both legs. This CM drop provides the energy pulse required to start the turn.

Push off with the left foot to commence a small vertical axis CCW rotation about the right heel in combination with a 45 degree horizontal axis rotation about the right heel. The right leg rotates about its own axis so that the right foot does a net 90 degree counter clockwise (CCW) vertical axis rotation provided that the right ankle has sufficient flexibility.

**CONTINUING MOVEMENTS:**

Push off with the right heel to half step left toward 9:00 o'clock with the left leg and execute a left arm gedan block/strike with the hips in hamni toward 9:00 o'clock. The right leg remains partially loaded to enable a follow-up right hand step-punch.

**JKA MOVEMENT VARIATIONS:**

There are some senior persons who when executing the first turn of Heian Shodan do just a 45 degree vertical axis rotation of the right foot about the right heel. This change in foot position allows a long reach left arm gedan block/strike without requiring right ankle flexibility. However, this change reduces the right leg energy that is available for driving the body CM over the left leg Midpoint Fully Loaded Position (MFLP) during the subsequent right leg full step.

**COMPARISON OF FISHER METHOD TO JKA METHOD:**

The important differences between the Fisher Method and the JKA Method with respect to executing this turn are:

1. In the Fisher Method the vertical axis of rotation is through the body CM whereas in the JKA Method the vertical axis of rotation is through the right heel. Hence the Fisher Method has a smaller moment of inertia about the vertical axis of rotation and provides a faster turn and a faster reverse punch;

2. The Fisher Method moves the right heel about 17.7 cm forward toward 12:00 o'clock thus positioning the hips at the end of the initial movement phase in shoman to the left instead of hamni to the left;

3. The Fisher Method during the initial movement phase moves the right heel about 17.7 cm further away horizontally from the vertical axis through the body CM, thus enabling a greater horizontal force vector component and hence greater horizontal acceleration during the continuing movement phase;

4. The Fisher Method positions the hips in shoman to the left instead of in hamni to the left to provide more defense and counterstrike options.

5. The Fisher Method positions the right foot to better engage the right leg and right ankle for providing maximum energy for the follow-on technique which involves driving the CM over the left leg MFLP during the subsequent full step-punch. The JKA method does not initially load the right ankle.

However, the Fisher method relies on increased ankle flexibility. Without such ankle flexibility, for a reverse punch counterstrike the Fisher method requires rapid rear foot repositioning in order to match both the speed and reach of the JKA method.

Adoption of the Fisher method implies a conscious decision to improve ankle flexibility and to give enhanced power and speed at shorter ranges and enhanced acceleration for the following full step-punch priority over maximum gedan block/strike reach.

**COMPARISON DETAIL:**

In Fisher Shotokan the initial position is with the feet pointing straight ahead. At movement commencement the right foot is turned 90 degrees CCW about the ball of the right foot which moves the right heel about 7 inches forward and about 7 inches laterally further away from the vertical body axis. This heel repositioning increases the horizontal component of the loaded right leg force vector from the right heel to the body and minimizes the lateral CM movement during the turn required to maintain normal lateral leg spacing. The increased horizontal force component causes higher horizontal body acceleration and hence more potentially deliverable energy. The unloaded left leg follows the hips to minimize the required lateral CM movement during the turn while maintaining natural side to side leg spacing.

In the Fisher Method of executing the first turn in Heian Shodan, at the end of the loading phase the legs are naturally spaced to allow hips shoman, whereas in the JKA method natural leg spacing is not achieved until the CM and the lead leg have revolved about the rear heel. The lateral CM movement in the JKA Method is very much larger than in the Fisher Method. The increased lateral CM movement together with a smaller horizontal force vector makes the JKA turn slow as compared to the Fisher turn.

Another problem with the JKA Method for executing the first turn of Heian Shodan is that the the potential reach of the reverse punch option (during the set motion) before any CM movement is not as great as in the Fisher Method. In the Fisher Method the initial reach is longer due to the hips being in shoman rather than hamni, even though the rear heel is seven inches further back. In the Fisher Method the knees, feet and hips are all pointed at the target at the end of the loading phase. The right hip can then rotate CCW about the left hip to add additional reach and power for execution of a right hand punch.

When the full step with the right leg is made after the first turn in Heian Shodan, the Fisher Method reach is longer than in the JKA Method because in the Fisher Method the right leg, right foot and hips are more favorably positioned with respect to the target and the ankle and calf muscles of the right leg can be more fully engaged to provide more energy. This extra energy allows a rapid drive over the MFLP, unlike the JKA method which has an empty back leg in zenkutsu-dachi.

If the opponent is too close the Fisher Method turn can be almost instantaneously modified to a backwards rotation on the balls of both feet to gain a small amount of distance.

Both the Fisher Method and the JKA Method are speed limited by the time required to execute the CM drop. At the end of the CM drop in the Fisher Method the body is a few inches further away from the opponent and is better positioned to counter attack.

**HEIAN SHODAN ANALYSIS:**

The following numerical analysis reverse punch time and range are used for performance comparison. A reverse punch is used because a step-punch is more difficult to mathematically quantify.

**COMPLEX BODY MECHANICS:**

Reverse punch range is a complex function of body mechanics. It is easier to demonstrate the relevant phenomena than to explain it. Stand upright in the initial position with your heels at shoulder width, feet pointing forward. Rotate your left foot 90 degrees CCW about your left heel. Rotate your right foot 45 degrees CCW about your right heel. While keeping your body upright lower your center of gravity until your legs are fully loaded. Punch with your right hand in the direction that your left foot is pointing. Note the exact reach of this punch. Return to the initial position.

Now execute a Fisher Method 90 degree CCW turn. Check that your right foot is pointing in the same direction as your left foot. Note that your right arm reverse punch reach in the direction that your left foot is pointing increases about two inches (5 cm), even though the right heel is about 17.7 cm further away than before. This extra reach is a result of complex body mechanics related to hips being shoman rather than hamni.

**CO-ORDINATES:**

For the purpose of this analysis I will use measured distances taken from my own body. The co-ordinate system will be X, Y, Z where X is horizontal distance forwards towards 12:00 o'clock, Y is horizontal distance sideways towards 9:00 o'clock and Z is the vertical axis through the initial centre-of-mass (CM) position. Z = 0 at floor level. The initial CM position is at X = 0, Y = 0, Z = Zo. The initial left heel position is: X = 0, Y = Ylo, Z = 0. The initial right heel position is X = 0, Y = Yro, Z = 0.

For me the measured values are:

Zo = +1.143 m

Ylo = +.172 m

Yro = -.172 m

**FISHER METHOD:**

The initial position is standing upright facing forward. Feet point forward. Heels are:

(Ylo – Yro) = 0.344 m

apart. The CM height (top of pelvis) is Zo = 1.143 m above the floor.

To execute the loading movement simultaneously rotate 90 degrees CCW on the heel of the left foot, rotate 90 degrees CCW on the ball of the right foot and drop the CM to the right leg fully loaded position. Simultaneously block a punch to your head by sweeping it past your right ear with your left palm and reverse punch with your right fist. The CM remains on the Z axis. There is no horizontal CM movement. The body is upright. The lower body has rotated 90 degrees CCW. The lowered CM height (top of pelvis) is at Z = Za. The reverse punch extends horizontally in the Y direction from the Z axis to Y = Ypa. The right heel has moved from X = 0, Y = Yro to X = Xra, Y = Yra. The left heel remains at Y = Ylo.

For me the measured values are:

Za = 1.080 m

Ypa = .940 m (= 37 inches)

Yra = -.349 m (=13.75 inches)

The minimum time Tz required to execute this movement is governed by the acceleration of gravity Ag where:

Ag = 9.8 m / s^2.

The appropriate formula is:

Dz = (Ag Tz^2) / 2

or

Tz = (2 Dz / Ag)^0.5

where:

Dz = (Zo – Za)

Hence:

Tz = (2 Dz / Ag)^0.5

= ( 2 (Zo – Za) / Ag)^0.5

= [ 2 (1.143 m – 1.080 m) / (9.8 m / s^2)]^0.5

= **.113 s**

To execute the half step movement lift the left leg and extend (unload) the right leg to drive the CM horizontally in the positive Y direction (toward 9:00 o'clock). The force vector is from the right heel to the CM. This force vector can be resolved into a vertical force vector Fz that must be equal to the body weight and a horizontal force vector Fy. The horizontal force vector causes horizontal acceleration.

Let M be the body mass. Then the vertical force vector is:

Fz = M Ag

The linear dimensions give the initial horizontal force vector as:

Fy = (-Yra / Za) M Ag

The resulting horizontal acceleration Ay is:

Ay = Fy / M = (-Yra / Za) Ag

As an alternative to immediate punching the punch can be delayed until the right leg is almost completely straight. The maximum reverse punch range is limited by the flexibility of the right ankle. On me this range is Ypb where:

Ypb = 1.041 m = 41 inches

The time Ty required to move the CM the horizontal distance Dy = (Ypb – Ypa) while keeping the CM at a constant height is:

Ty = (2Dy / Ay)^0.5

= {2 (Ypb – Ypa) / [(-Yra / Za) Ag]}^0.5

= {2 (1.041 m -.940 m) / [(.349 m / 1.080 m) 9.8 m /s^2]}

= **.253 s**

Hence the time T required for me to compress, turn, expand and punch out to 41 inches (1.041 m) with the Fisher turn method is:

T = Tz + Ty = .113 s + .252 s = **.365 s**

**JKA METHOD:**

The initial position is standing upright facing forward. Feet point forward at 45 degrees to the main embusen. Heels are Ylo – Yro = 0.344 m apart. The CM height (top of pelvis) is Z = Zo where:

Zo = 1.143 m above the floor.
The initial position is CM at:

X = 0, Y = 0, Z = 1.143 m.

To execute the loading movement drop the CM straight down to the legs fully loaded position. The CM is now at Z = Za = 1.080 m. Simultaneously rotate the left foot 45 degrees CCW about the left heel, rotate the right foot 90 degrees CCW about the right heel and rotate the hips CCW as far as possible subject to the right heel remaining at Y = -Yro. The CM does not move in either the X or Y directions. Simultaneously block with the left arm and punch in the Y direction with the right arm. The punch reach is limited by body mechanics to Y = Ypc = .889 m from the Z axis, about .051 m less than in the Fisher Method.

For me the measured values are:

Za = 1.080 m

Ypc = .889 m = 35 inches

The minimum time Tz required to execute this movement is governed by the acceleration of gravity Ag where:

Ag = 9.8 m / s^2.

The appropriate formula is:

Dz = (Ag Tz^2) / 2

where:

Dz = Zo - Za

or

Tz = (2 Dz / Ag)^0.5

= (2(Zo – Za) / Ag)^0.5

= [ 2 (1.143 m – 1.080 m) / (9.8 m / s^2)]^0.5

= **.113 s**

This loading takes the same time as the loading in the Fisher method.

Now unload the right leg while keeping the CM height constant. The vector analysis is similar to in the Fisher method except that in the JKA method:

Fy = (-Yro / Za) M Ag

Ay = Fy / M = (-Yro / Za) Ag

Dy = (Ypb – Ypc)

Ty = {2 Dy / Ay}^0.5

= {2 (Ypb – Ypc) / (-Yro / Za) Ag}^0.5

= { 2 (1.041 m - .889 m) / (.172 m / 1.080 m) 9.8 m / s^2}^0.5

= **.441 s**

T = Tz + Ty = .113 s + .441 s = **.554 s**

Thus, all other factors being equal, a reverse punch to Ypb = 41 inches (1.041 m) will be consistently:

(.554 s - .365) = **.189 seconds**

faster using the Fisher Method 90 degree turn than the traditional JKA Method 90 degree turn.

**EFFECT OF INITIAL HEEL SPACING:**

Readers should note that the time advantage of the Fisher method is dependent on the initial heel spacing. In my case the ratio of initial heel spacing to CM height is:

(Ylo – Yro) / Zo = (+.172 m - ( -.172 m)) / 1.143 m = .301

In the photographs in the second edition of Karate-Do Kyohan this ratio appears to be 12 / 25 = .48

In the photographs in the official manual of the JKA this ratio appears to be: 16 / 40 = .40

Clearly in the past the Japanese adopted much wider initial shizen-tai stances than we are accustomed to today. It is possible that in the past the ratio of leg strength to body weight for Japanese karate-ka was larger than for us today.

On me a ratio of ratio of initial heel spacing to CM height of .40 would imply an initial heel spacing of:

(Ylo – Yro) = .40 Zo = .40 (1.143 m) = .457 m = 18 inches

Increasing the initial heel spacing will reduce the time advantage of the Fisher method as compared to the JKA Method. However, increasing the initial heel spacing requires a substantially larger leg strength to body weight ratio to achieve the theoretical best speed.

Repeating the above calculations for the Fisher method with an .457 m initial heel spacing gives:

Tz = **.113 s**

Ty = (2Dy / Ay)^0.5

= {2 (Ypb – Ypa) / [(-Yra / Za) Ag]}^0.5

where:

Yra = ((.457 m)/ 2) + .178 m = .407 m

Ty = {2 (Ypb – Ypa) / [(-Yra / Za) Ag]}^0.5

= {2 (1.041 m -.940 m) / [(.407 m / 1.080 m) 9.8 m /s^2]}^0.5

= **.234 s**

Hence the minimum time T required for me to drop, turn and punch out to 41 inches (1.04 m) with the Fisher method and an initial 18 inch (.457 m) heel spacing is:

T = Tz + Ty = .113 s + .234 s = **.347 s**

Repeating the above calculations for the JKA method with an initial heel spacing of 18 inches (.457 m) gives:

Yro = .457 m / 2 = .2285 m

Tz = **.113 s**

Ty = Ty = {2 Dy / Ay}^0.5

= {2 (Ypb – Ypc) / (-Yro / Za) Ag}^0.5

= { 2 (1.041 m - .889 m) / (.2285 m / 1.080 m) 9.8 m / s^2}^0.5

= **.382 s**

T = Tz + Ty = .113 s + .382 s = **.495 s**

Thus with an initial heel spacing of 18 inches (.457 m) a reverse punch to Ypb = 41 inches (1.04 m) will be:

(.495 - .347) = **.148 seconds**

faster using the Fisher Method turn than the traditional JKA Method turn. Hence, subject to sufficient leg strength, a small but significant fraction of the Fisher Method advantage is lost if the initial stance is proportionately wider than my natural stance.

At this point it is appropriate for me to indicate to the reader that I am exceptionally stiff. If I had sufficiently flexible ankles Ypb would be 48 inches instead of 41 inches, giving the Fisher Method a time advantage at a distance of 48 inches of over 0.2 seconds in all cases.

**JKA METHOD REVERSE PUNCH RANGE:**

The JKA Method reverse punch range can be extended to about 55 inches without lifting the right heel from the floor. Thus the JKA Method has a reverse punch reach advantage in the range 48 to 55 inches. However, that range advantage may be offset by the time advantage of the Fisher Method.

**LIMITATION OF THE FISHER METHOD:**

A limitation of the Fisher Method is that with my limited ankle flexibility, my reverse punch range with my right foot pointing forward is limited to about 41 inches, whereas with more ankle flexibility this reverse punch range has the potential to be 48 inches with the Fisher Method and extends to about 55 inches with the JKA Method. In order for the Fisher Method to remain superior in the range 41 to 48 inches I must move my right leg forward at least 7 inches and replant it within much less than the .148 second advantage period. This minimum required leg advance speed is:

(7 inches / .148 s) (.0254 m / inch) = 1.20 m / s

In principle that leg advance speed is possible. My maximum CM velocity is:

Ay Ty = Ay {2 Dy / Ay}^0.5

= {2 Dy Ay}^0.5

Recall that:

Ay = (-Yra / Za) Ag

Hence:

Ay Ty = {2 Dy (-Yra / Za) Ag}^0.5

= {2 (1.041 m -.940 m)(.407 m / 1.080 m)(9.8 m / s^2)}^0.5

= 2.29 m / s

Hence the CM momentum should drag along the rear leg sufficiently quickly to meet the required speed criteria. However, much of the Fisher Method time advantage is lost. It would be better for me to improve my ankle flexibility. An alternative is for me to sacrifice power at long range by lifting my rear heel and going onto the toes of my rear foot.

**SUMMARY:**

Distance to the target is measured from the initial CM position. In the distance range 0 to 35 inches neither the Fisher Method nor the JKA Method provides a significant initial reverse punch reach or time advantage. In the distance range 35 inches to 41 inches the Fisher Method provides an initial reverse punch a 2 inch reach advantage and a 0.00 to 0.19 s time advantage. In the distance range 41 inches to 48 inches the time advantage of the Fisher Method further increases but realizing this time advantage requires improved ankle flexibility.

The Fisher Method has the distance disadvantage that at the end of the loading phase the right heel is about 7 inches further away from the opponent than in the JKA Method. However, at ranges up to about 48 inches this disadvantage is out weighed by the improved reverse punch reach and improved horizontal acceleration. Improved horizontal acceleration results in greater deliverable kinetic energy.

In the distance range 48 to 55 inches the JKA Method enables a longer reverse punch reach without movement of the rear heel. However, the Fisher method can match this range by changing the right foot ground contact point from the heel of the foot to the ball of the foot, while still maintaining its time advantage. This time advantage is typically 0.15 to 0.2 seconds.

The time advantage of the Fisher Method over JKA Method decreases as the Shizen-tai heel spacing increases. However, the required leg strength to body weight ratio also increases as the initial heel spacing increases.

**CONCLUSION:**

**Notwithstanding the official JKA manuals and other karate texts advanced karateka should use the Fisher Method for executing the first turn in Heian Shodan.**

This web page last updated January 23, 2011.

Contents | Blogs | Introduction | Fisher One Page | Contacts | Links |
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