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Vertical punches say more power is transfer to the target when using a vertical punch

To be effective, the force of a punch must be transferred from the body into the upper arm, forearm, wrist, hand, and into the target. This force is generated by muscles, but it is transferred through bone. Without bones to act against, the power generated by muscles would be useless. If the bones are misaligned at the joints or the joints are not angled properly, the force transfer will be reduced and injury to the joints may occur.

For the purpose of this discussion, we will consider just the bones in the arm. The single large upper arm bone, the humerus, makes contact at the elbow with two forearm bones, the radius, the larger of the two, and the ulna. The contact the humerous makes with the radius is larger in area, much stronger, and more stable than with the ulna so the radius  transfers more force down the arm than the ulna. At the lower end of the arm, the contact the radius makes with the wrist is larger in area, much stronger, and more stable than with the ulna so the radius transfers more force to the wrist than the ulna. When the fist is extended, the radius is naturally in line with the first two knuckles of the hand. The wrist cannot be positioned to make the radius align with the last two knuckles. The Ulna is in line with the middle two knuckles. The only way to line the ulna up with the first two knuckles is to drastically bend the wrist, which is would cause injury to the wrist in a punch. The only way to line the ulna up with the first last knuckles is to bend the wrist, which means the radius is not effectively transferring its greater force.

Vertical punchers say that, as force is transferred down the radius and ulna, a band of very tough connective tissue at the wrist, the interosseous membrane, connects the ulna and radius and causes the forces moving down the two bones to be shared at the wrist. They say that the degree of force transfer via the interosseous membrane depends upon how tight it is, which depends on the amount of twist in the forearm. The tighter the membrane, which they say occurs in a vertically oriented punch, the better the forearm bones share the energy transfer. However, force is transferred through the bones not through connective tissues. All the connective tissues do is hold the bones in position so they make contact. As long as the bones are in contact and stay in contact, the tightness of the interosseous membrane is irrelevant.

Vertical punchers say the vertical punch uses the correct muscles

Vertical punchers claim the vertical punch uses the triceps muscle, which is mostly used for pushing, or punching, while the horizontal punch uses the bicep muscle, which is mostly used for lifting, not punching. This claim is absurd.

Conclusion

It does not take a lot of input from the instructor or a lot of practice by the student for the student to learn to punch in natural motion. To gain any effectiveness from holding the hand in an unnatural position requires a lot of instructor input and student practice.

As I have stated before, my goal in teaching is that each student leaves a class better able to defend him or herself than before he or she entered the class. When a first day beginner leaves my class and is attacked in the parking lot, he or she will be better able to perform the natural horizontal punch that they were born with, and not be confused with trying to punch vertically.

Taekwondo also has it illogical teachings. A front stance is a natural stance that any beginner may perform easily, however, for pattern performance purposes, we teach that the rear leg should be straight and the rear foot should be parallel to the front foot. This is an unnatural position since it take a conscious effort to keep the rear leg straight and the rear foot twisted and it puts undue strain on the Achilles tendon, but the power that be have determined that this is a more visually pleasing way perform the stance while performing a pattern. When performing patterns, a student is required to maintain constant, conscious thought to maintain this type of stance. The rear knee wants to bend naturally and the rear foot naturally wants to angle outward at about 30 degrees. I have been able to rationalize teaching this way of performing a front stance (straight leg and parallel foot) since the stance is only used this way while performing patterns, since the front stance is seldom used in fighting, because the stress it puts on the legs helps make them stronger, and because the concentration required to maintain the stance in this manner helps students concentrate, which helps them while learning other techniques. If the front stance were taught this way as a fighting stance, I would have a problem with teaching it and have to look for another school.

Practically anything may be practiced in patterns. Patterns are the history books of the martial arts. They memorialize the roots of the arts and help carry on the traditions of the arts. Most of the techniques used in patterns are old and outdated for use in modern day fighting, but they preserve the history of the arts. We may learn from history but that does not make what was taught in the past correct, nor does it make it relevant in modern times. Since patterns are more of a mental exercise than a physical one, performing patterns of any style and using the techniques of that style will aid your development in your style, since you are learning to concentrate and use precise muscular control. In my experience, students who do well in patterns are usually effective fighters, but effective fighters do not necessarily do well in patterns. However, this does not mean that the techniques used in patterns have any relevance to actual modern day fighting. There is the way things are performed in patterns, and then there is the way they are performed in fighting. The pattern performance and sparring are two different entities, so they do not inter with each other. If you are proficient at driving a motorcycle, it does not interfere with you ability to drive a car.

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