I've been told that I don't have much power behind my punches and that push-ups are a good way to improve this. Is there a good push-up route that could be done at the beginning or the end of the day that involved more than just the standard push-ups?
For all the talk about kinetic linking (like it's something we didn't already know for centuries), the truth is really rather simple: pushups, while good for developing muscle and overall personal health, are really ancillary to the development of raw punching power. Further, the tendency to isolate the arms by maintaining rigidity in the rest of the body can lead to a loss of dynamic motion in the whole body, which can be detrimental to the dynamic movement required by a strike.
Consider for a moment the pushup (in any format; it's really irrelevant):
This seems, logically, to put an emphasis on extending the arm, which is correct. This builds "push" muscles, which allow you to extend your arm with force, allowing you to push heavier objects. Unfortunately, a side effect of this is that you're also pushing with only the arm.
This states that Average Power is equal to a change in work over a period (change) in time.
If we take this further:
∆W = (m • a) • ∆s
Or the change in Work is a function of a change in displacement times the combined mass times acceleration.
So, in terms of a strike, we can understand this much:
I don't want to discourage strength training; you can develop explosive energy with clapping pushups and the right kind of training. Pushups in general, however, are only minimally useful, and I would hate for your expectations to be greater than your output from the time invested.
If you are finding them hard from a plank position, do them from your knees. The plank is a good one to re-enforce your core which you will use when you punch. Pull ups and chin ups will help as well. A pull up bar can help you do push up and dips, plus they are not that expensive. Make sure you do triceps and biceps as well -- do not do just one.
There is push up challenge on the net somewhere but the number increase do get silly after week 3/4. Body Rock TV or Rudy Reyes sites should have some interesting exercises. Do be careful when you do then not to hurt yourself. Remember, little by little does the trick. Remember to have days off to let your muscles recover. Eat well (proteins) and hydrate yourself. Eggs are good and filled with goodness.
In all of those boring exercises, you need to find some way to motivate you: goals are great! Set yourself some goals (do X push ups in Y or do X+1 today where X was yesterday or keep doing them for length of favourite song). They have to be small goals that you can do again and again.
There are actually a lot of different pushup variations that can help build the base muscle. Convict Conditioning (ignore the marketing) has an excellent one that goes from wall pushups through a ten-step progression to one-armed pushups, with standards at each level for when you should advance to the next more difficult pushup variety.
There are also other pushup variations such as decline pushups that can help target specific muscles that might help here.
Once you have a good base of strength–and you will definitely want to take the time to build a good base–for punches specifically you are probably going to want to move into plyometric pushups, e.g., clapping pushups, other variations, etc. These are useful for the development of what's called "explosive strength" and some coordination around these movements.
Also don't forget to balance these out with pullup variations of some sort, since you don't want to just work on one set of muscles.
Other ideas that work some of the same muscles are handstand pushups (also in CC) and a variety of gymnastic exercises (generally involving parallel bars and/or rings) that you can do that can help.
You generate more power in your punches via Kinetic Chaining or Kinetic Linking of your legs through your torso/core into your arms then just raw arm strength. Some good Kinetic Chaining exercises are push ups, pull up and chin ups. Not because they work on your arm or arm strength but because they can build up all the muscles that link the chain (i.e. your core) between your arms and your legs.
My personal routine for push-ups is that I do sets of 10, throughout the day. Wake up, do 10, before I leave for work, another 10, at lunch, another 10, when I get home another 10, before I go to bed a final 10. As Sardathrion said in his answer if you can't do them from the toes (plank) do them on your knees, your still working the muscles. Don't cheat yourself, go all the way down (hovering your chest above the ground), hold for a second and push back up. Try doing 50 a day, either on your knees or normal, then start doing more reps per batch.
A good core and stance will lead to more powerful punches then someone with big arms. My friend has much smaller arms then I, but a ripped core and perfect stance (bent kness, toes, forward, ball of foot, good extension, rotation, etc) and throw those punches like cannons.
I'm going to go ahead and sidestep the pushups part specifically and answer the question about strength training for punching power instead.
If you check out http://punchingpower.org/the-falling-step/ and go through all the videos, you'll come across a hook punch one that involves doing a swinging motion with medicine balls. That's a very specific resistance training exercise that's applicable to punching. The entire series also goes into detail about the technical aspects of throwing a punch for increased power.
Also, when you break down the technical aspects of the punch you'll see there's a lot more to punching than the pushing motion of a pushup. Of course it certainly wouldn't hurt to do pushups, but you'd have to balance it off with a pulling motion (chin ups or pull ups). You'd also want a twisting motion (the aforementioned medicine ball exercise for example) and a stepping or lunging motion (unsurprisingly, lunges, bulgarian squats could work too).
I found that push-up with fist (rather than palm) helps me a lot in fixing my wrist and getting my punch in correct forms.
A punch should hit target with the knuckles of the index finger and middle finger. (straight punch in taekwondo and karate) While doing push-up, You should roll your fist forward so that only these 2 knuckles (and the first part of these fingers) touch the ground. No weight should be pushed onto the ring finger and small finger.
The elbow, the wrist and the first 2 knuckles should form a straight line, both while doing push-up and during punch. Through practising push-up with fists I learnt the feeling of the force of impact of hitting target.
The force should be delivered from core. The arms and fist should be strong enough to delivered that force.
Push-ups are not the concern here. Instead, you are looking at a deficit of one or more of the following: strength, power, conditioning, strength-endurance, and technique. First, let's define those terms.
Strength is the ability of the body to produce force. Power is the ability of the body to produce a given force quickly, and is a derivative of strength. The human body moves through the use of muscles, so although technique is important, one must remember that the muscles are a major prerequisite of strength and power. Someone who is strong and powerful might have poor technique and therefore not punch hard, but someone who is weak will be limited in absolute terms in how hard they can punch, because their body simply cannot produce the force.
Conditioning is how in-shape you are, or how well you can maintain a given level of exertion in a particular activity. Someone in poor boxing condition will quickly tire during pad or bag work, or during sparring or a fight. Strength-endurance is related, being the ability to continue producing force over a stretch of time. For instance, someone with poor strength-endurance may be able to punch hard and quickly for a minute before their punches become slow and weak. This attribute is a derivative of strength, and is affected by one's conditioning.
Technique is the maximally efficient harnessing of these attributes to produce results.
Adding Power to Punches
Any or all of these might be the concern in someone whose punches lack power. Push-ups could help a little with some of these attributes, but aren't really the optimal solution.
You need to evaluate which of these aspects is lacking in yourself, and develop it. If you're weak, then basic resistance training the necessary first, even if your technique needs work too, because your strength puts an upper limit on what your technique can maximize. Basic resistance training would include barbell and dumbbell exercises such as presses and bench presses, as well as squats, chin-ups, and deadlifts.
If you're strong but not powerful--if you have a big and slow bench press, but you push your punches--then speed work with resistance is called for. Push presses, throwing heavy implements, power cleans, and jumping are good training in this area. So are clapping push-ups, though only if you already have a good strength base.
If you're throwing awesome punches at the beginning of class, but later they're plodding push-punches later, then strength-endurance work might help. High-rep sets of push-ups could be called for, again, only if you have a good base of strength and power. More drilling and long rounds of working your punches might help. This is one area where I'm a little bit at a loss--I'm less familiar with the ideal training for this attribute.
Technique and conditioning can always use work, so keep training hard, keep refining your punches and your footwork, keep getting feedback from your instructor, and do tons of activity-specific conditioning like hitting the heavy bag, hitting pads, sparring and drilling with gusto.