Again let us first consult the official handbook of the German Riding Federation:
“The horse’s propulsive force, developed by the quarters, can only be fully utilized in forward direction if the horse moves ‘straight’. A horse is ‘straight’ if the hind feet follow exactly the same line as the front feet. Only then can the rider transfer more weight evenly on to both hind legs increasing their carrying power. Most horses’ bodies are naturally crooked. This is even more pronounced because a horse is narrower in his shoulders than in his hips. Most horses move with their right hind leg outside alongside the track of the right front leg. The propulsive force of this right hind leg moves diagonally across to the horse’s left shoulder, transferring additional weight on to the left front leg, and giving the rider a much stronger contact on the left rein. In this case the horse will also lean against the rider’s right leg. Occasionally the horse is crooked in the other direction, with corresponding results on the other side.”

The Principles of Training, page 174
Straightness is the horseman’s eternal chore, no matter how educated the horse, he will always have that tendency to revert to his natural crookedness, he will always need the assistance of the rider to make him straight.
Jo Hinnemann is a rider as well as a trainer, he knows how much work it takes: “Every horse naturally has an easier side. Just as every person is naturally right or left handed, so is every horse. We continue to emphasize that a rider’s job is to gymnasticize his horse, to attempt to alleviate this natural crookedness through correct work. A crooked horse can never move entirely in balance and always has an escape door through which the energy can’t optimally flow through from back to front. He can never correctly carry weight on his hindquarters. That’s why straightness is a very essential part of a horse’s training.”
(The Simplicity of Dressage, page 87)
As Clemens points out, riding your horse straight is not just riding straight lines, the horse has to be ‘straight’ on his bended lines as well.
“It is very important that the horse basically tracks up from behind, with the hind legs in the same direction as the front legs – that is straightness.”
“Basically you have to ride your horse straight, on circles or loops or whatever. The hind legs must exactly follow the direction of the front legs. On a straight line, or a bending line, on a circle, that never changes, the hind legs step in the same direction as the front legs. The saying in Germany is ride your horse forward and straighten it. If you ride your horse more forward, it will make it easier to get the horse straight.”
“To make the horse straight you think of putting the forehand in front of the hindquarters. If you are cantering to the left, and the horse swings his quarters in, then you basically bring the shoulder fore, in line with the hindlegs, and that applies in all straightness. Adjust the front legs to the hind legs – not the hind legs to the front legs.”

“We also use our lateral work, or bending to help us straighten the horse. Basic leg yielding is a wonderful exercise to teach the horse to respond, to move off one leg, but all the lateral work is necessary so you can control your horses body. I think leg yield is fantastic for half pass as it frees them up to cross over, it teaches them to go off the leg, and it is a very good movement to counter evasion. If you try to collect and the horse goes against your leg, immediately turn that into leg yielding to the other side. It is one of the most useful exercises I have found in training horses. A lot of people, they come down the centre line and they want to piaffe, and the horse takes off, then do leg yield to the opposite side from the one he wanted to take off to, maybe even with a few piaffe steps in it, and you can correct the horse. Instead of trying to stop the horse taking off, you put it into a movement, and the movement is leg yield.”

Right now Judy is demonstrating her control of Frontier’s body with some wonderful lateral work, the shoulder in flowing effortlessly into the half passes.
“When we ride shoulder in it is important to maintain the same forwardness, in the same trot. If the trot was a 7 or an 8 before, the shoulder in will be kept a 7 or an 8, because the pace remains the same in the shoulder in.”
“95% of riders when they come to ride shoulder in or half pass, suddenly go into a different gear, they don’t maintain the forwardness, or the big strides – and so the score goes down. Look at the half pass, see how Judy is really concentrating on the trot, the main thing in the half pass strides is the beat, and to maintain the same quality of trot – that’s where most people fall down. In the half pass the shoulder must always be leading, open the inside rein to allow the freedom of the inside shoulder. The shoulder must be a little in front.”
“Unless the horse is through, accepting the bridle and on the aids, he will never go straight. Every day you have to concentrate on making your horse straight, they are always finding ways to go crooked, no matter how long or how well you train them.”
Judy had moved on to a little counter canter:
“Counter canter is good to confirm aids, and teach the straightness. Many riders try to ride the counter canter with a very big flexion to the inside because they are not sure they can hold the horse in the counter canter, but this means the horse is not really on the aids. The rider should be able to ride the counter canter, with just a little bend to the inside – the rider should even be able to flex the horse to the outside and not lose the counter canter. The horse must be on the aids if it is to go straight.”
“And straight if it is to go on the aids…”

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