The Lead Hand Power Punch
The science behind punching, or hitting with the lead hand, can be defined as the ability to generate maximum power while exerting minimum energy and effort. This definition could also be expressed in terms of ' Combat Efficiency and Effectiveness'. Punching is the bedrock foundation of almost all methods of realistic combat or self defence, and a good fast, powerful and explosive lead hand shot is not only your bread and butter, moreover could be your main attacking tool.

The concept of straight punching is simple, although it takes time and personal experimentation, by continual impact battery to perfect and maintain.
Through my research, I have discovered that early pugilists tended to punch more with the bent arm, rather than utilise the straight punch. James J Corbett is credited as being one of the first fighters to scientifically perfect the straight punch with the lead hand. However, it is logical to assume that other fighters preceding Corbett were aware of direct straight punching.

Lead hand straight punching is theoretically faster than hooking (although in practice and on the receiving end, you could hardly notice the difference, especially at close range) and is more accurate. One thing is almost a dead cert; an untrained aggressor, in a bar room brawl for example, will vent his anger with a wild swing as opposed to a straight punch.

When shooting a lead hand power punch, it disturbs your balance less, and recovery is quicker, when compared to hooking, making for a high rate and diversity of punching. As in most mechanical actions leverage and motion are prerequisite factors, this translates into fighting science as balance in motion and body mechanics / structure, and technique.
The object of the lead hand power punch is besides being as fast as you can, to put as much mass behind each shot as is physically possible. (There is a trade off equation here of speed to power ratio, against impact time, experiment on the heavy bag and note your results).
Lets not get confused here, we are talking about street-fighting and self-defence, not scoring points in a boxing ring with a fast flashy jab. To clarify the point and summarise, when utilising the lead hand power punch we should actually be hitting the opponent with our body mass (in motion), the arms just being communication lines of the generated force.
The weight behind the lead hand power shot is achieved by a combination of linear and rotary and motions, (application of kinetic energy). This equates to stepping / exploding forwards, whist simultaneously rotating both your hips and shoulders.
In execution the fist should hit the target a fraction of second before your lead foot lands on the ground, and shoulder, hip rotation is fully completed. Thus, the mass of body weight in forward and rotating motion is transferred directly into and behind the fist, enhanced with yet another potential force (gravity), landing on target with exceptional potency.
The rotating and twisting of your hips and shoulders is derived from your rear foot, (this is the key) which initiates the motion. (Centrifugal force)
The energy is started from you twisting foot / ankle, through to your knee, which is transferred up and through your hip, which eventually is relayed into you shoulders, were it can be switched into useful linear 'punching' power.
This description of rotation or twisting is referred to in some old boxing manuals as, overlapping and concurring circles.
The concept of rotation, with the addition of a step forwards, with the right timing, will result in a powerful jarring punch, which will really stun your opponent, and ring his bell for sure.
Although the concept is relatively easy to absorb and digest, the application is somewhat harder to put into practice. Don't expect to get this power punch in five minutes, it will require a bit of experimentation and self-analysis, however once you get the timing, (which is specific) down, you will be greatly impressed with your new found whacko! Power punch.

Advanced Details
When you shoot out this lead hand power punch let your arm fly out like a whip, keep your arm relaxed and flexible. Imagine you have a weight on the end, like holding a big stone in your hand. Your arm stiffens at the moment of impact, from you wrist, elbow and shoulder.
Do not be tempted to push out your arm like playing a trombone, as amateur boxing coaches tell you.
Ensure you follow through the target, do not punch at it but through it with an explosion of combined energies.

Speed Improvement
To make improvements to your newfound power and to make it into a real 'stinger', you will have to work on total body speed. Speed is the only variable within the equation, which can be changed.
The following physical formula can express this concept: -

Impact = Mass x Speed
Mass = Weight of your body in Kg / sq cm
Speed = Meters per second

Work on initiation speed, arm speed; forward stepping speed, explosive speed. Isolate each area, and then start to combine.

Body Mechanics and Structure
The lead hand power punch will place a considerable amount of weight behind your fist, which will place considerable strain on your wrist, It takes training, on the heavy bag, and a few bent ricked wrists, before you get the conditioning down to deliver this shot at full all out power.
To use this punch safely and strongly, body mechanics dictates that you strike using a vertical fist, (or very slightly angled inwards). Don't try this with a horizontal fist, as you will almost certainly sprain your wrist. The contact points are with the lower three knuckles. Aim the shot by leading with either your little finger or your ring finger, which ever your preference is.
Your targets can be the nose, or the chin. (Front and sides)
Ensure that you withdraw the shot after contact, don't die on you target, and return back to an on - guard fighting position.

Training
     Heavy bag, 3 x 3-minute rounds. (For power, speed and body conditioning)
     Maize ball, 3 x 3-minute rounds. (Explosiveness and accuracy)
     Hanging paper, 3 x 3-minute rounds. (Snap and timing)
     Focus gloves, 3 x 3-minute rounds. (Timing, power, with footwork)

Conclusion
The lead hand power punch is an excellent street fighting / self defence tool, but like any thing in life you only get good by practice, so.... GO FOR IT!