<font face="Verdana, Arial" size="2">When I was going to push him directly, he just balked with all his strength and I felt like I am touching a rock. So I was impelled to change the vector of my strength and start to "swing" him (to the left and to the right
in different ways). This helped but not much and I am not satisfied with the result. </font>
A successful push is a result of good tingjin, stick, neutralization, seal and uprooting. If you don't get the precedings right your push will be less effective because your opponent will be able to resist it somewhat or retreat altogether. Watching a skilled hand push and you will notice as though there are no preset-ups preceding it but thats not true. A push is clumsy when you failed to siege that `split second' of defect in your opponent, which require good tingjin. Even when sieged, you must be able to transmit 100% of your force into your opponent in split second, which means you must be very song. A perfect combination of these will send your opponent flying all the times. Generally, you push when your opponent is moving backwards so that your pushing force can ride on his backward momentum. In other word, your push harmonize with his movement. If he is stationary or moving forward and you push, it will be less effective because your push will be agianst his body weight. Same when you swing him sideways, if he is not moving along your force, it will be less effective. To push a person 10-20 fts away, you must coordinate that push with his movement.
On a more subtle note, you don't push immediately when your palm touches him. If you do, you will hv to deal with his weight. When you touch, if it is soft you don't push because it may get neutralized. But if you felt stiffness, then gradually apply strength. This is when your tingjin and nien jin (stick) becomes very important. When you apply strength bit by bit and you felt he resist, wht shld u do? Most people will continue to push with more strength hence, the push though successfull will be clumsy and messy. From your note I guess you do that too.
What u shld do is actually to empty out just enough for his resistance to drop into empthiness. Having said that I do not mean you pull back your hands, you still stick to your target area and still applying strength however, this is not a pushing strength but sticking(nien jin) strength. Purpose is to trick him into putting more strength forward to oppose you. When he resist with strength forward, you empty out just enuf to let his strength falls into emptiness and he will subconciously pull back to stabilise himself. At this second during his retreat you add more pushing strength to destroy his balance. Once his balance and body weight is agianst him, you push with whole body sending him away.
These movements will be very obvious to naked eyes in the beginning and your opponent can feels it openly but when you become more skillful, the movements become smaller and smaller and to an untrained eye, there is no activity at all but a direct push. The skills involved are very subtle but nevertheless attainable with practise. At high level, even your opponent will not be aware of his own subconscious resistance that has been explored by you.
To achieve this you must look internal rather than external techniques. Get a partner to train with you this way...put both palms on his as in Ann. Apply a bit strength to the palms not to push but to induce him to resist. When your partner resist, adjust your pushing strength to minus his resistance with both palms still touching him with sticking jin. His resisting force will makes hin lost balance and as soon as he apply force to regain balance, you add on that force to make him overshoot his balance. Once he has overshoot his centerline you apply force to throw him out. At this point (beyond his centerline)any resistence force by opponent will actually add on to your force. Train this way until your movements become so small that almost like there have dissapp0eared.