For the other posts in the "Working Towards Softness" series, please see the sidebar. And, as always, please keep in mind that I am not a horse trainer, just a horse person who works in the best way I know how with my horses. There is no one right way to work with horses (although in my opinion there are wrong ways) and this is just how I go about it.
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I don't use lungeing or ground-driving with every horse - I myself don't start young horses under saddle where these skills, particularly ground-driving, are very useful. Even where I do use lungeing or ground-driving, I tend to use it only for a limited period of time until the objective I have is achieved - and the objectives may vary depending on the horse. I've had horses like Lily where a precautionary bit of lungeing was always advisable to check her mental and emotional status on that day, and even then lungeing was only done until she would offer up what I wanted - in her case it was two laps in each direction at each gait, where she was reasonably relaxed. I'll also use it with a more energetic or reactive horse after a long break to check in on their status, otherwise I rarely lunge or ground-drive.
When I lunge, I don't stand still in the middle of the circle, and I don't use a lunge whip. I just use the fuzzy-nose halter, no bit, and a lunge line - no side reins either. My objective is for the horse to be able to move, and make upwards and downwards transitions, simply off my body language and energy, sometimes backed up with a secondary verbal cue. I don't lunge my horses to burn off excess energy, and there's no mindless circling - if we're lungeing, we're working on something specific - but then my horses have the benefit of all-day turnout - lungeing for safety is certainly appropriate if your horse is stalled for most of the day. I move with the horse inside the horse's circles, and we also do some straight lines from time to time - you could call this one-line ground driving, if you'd like - obviously your horse needs to be responsive to your body language to be able to go in a straight line or move outwards from you. I walk slowly in a small circle when the horse is walking, and walk much faster in a somewhat larger circle when the horse is trotting - I try to match the energy level I want the horse to use. So, to slow down, I slow down myself and lower my energy. This to my way of thinking means that the horse and I are working together on the activity, rather than me standing still in the center and the horse doing all the work. I don't use side reins because I want the horse to have the ability to stretch down when the horse feels the need to, and also because I don't use lungeing to teach a horse to soften - I do that in-hand and under saddle (although you can work a bit on lateral softness when lungeing).
Here's an example of lungeing with a purpose involving Dawn. This was early on in our work, and we were working on our attention to one another and also her relaxation. I was looking for her to be able to maintain a gait, or do transitions up or down, off my energy and body language - this was to help her with her attention. I was also working with her on being able to let go with her neck to the inside in response to pressure from the line - this is her more difficult direction and in the picture she isn't there yet.
(There is also free-lungeing - think round pen work but with no round pen enclosure. I don't train my horses to do this, but I do have one who will free lunge - Drifter. This can be useful to work the horse at liberty and get the horse's attention focussed on you.)
Ground-driving is a skill that I wouldn't presume to try to teach in a post. The way I do it involves two lines and a fuzzy-nose halter. I don't use a surcingle. It does take some practice to avoid tangling yourself or the horse in the lines - using a surcingle reduces the risk of entanglement somewhat. I prefer not to use a surcingle due to the leverage effect it creates - no surcingle also makes it more easy for me to use an "opening" inside line to direct the horse in certain figures. I also rarely ground-drive using a bit because of the risk of injury to the horse's mouth if it steps on a line. One of the primary safety rules when either ground-driving or lungeing is to never hold the lines with a loop in them that could entrap your hand.
There are a couple of preliminaries to teach the horse before ground-driving. First, being able to tolerate lines around the legs and hindquarters - you want the horse to not panic and to be able to give to pressure on the legs from the lines and not fight or pull back. I do this by teaching "leading by the legs" - I start by taking a soft cotton lead rope and putting it around each leg and different heights - you want the horse to give to the pressure - eventually you should be able to lead your horse just with soft pressure on a leg. And you want the horse to be comfortable with lines on its sides and around its hindquarters. I usually work on this by standing next to the horse and taking the line that runs from the opposite side of the halter and moving it on the horse's back, then further back and so on until the horse is comfortable with the line around its hindquarters. Second, the outside turn. Hook a line to the halter on on side and run the line along the horse's side and around the hindquarters - you'll be standing on the opposite side of the horse from the side the line is attached to - stand far enough away so that when the horse turns, its hindquarters aren't too close to you. Put tension on the line - the objective is for the horse to follow its nose to the outside and turn around until it faces in the other direction.
Here are a couple of examples of ground driving. This is horse #8 from my series of 2009 Mark Rashid clinic posts (see the sidebar). This horse was being restarted under saddle, and was just being introduced to the bit again. You'll note that she runs her lines through the stirrups of her Western saddle - some people like to do it that way. You'll also note that she trails her lines behind her - I do this too as it makes shortening and lengthening the lines easier and avoids tangles.
And here are a series of photos from some ground driving work I did with Dawn when I started her back to work a year or two ago - in the second photo we're starting an outside turn, and in the third and fourth, we've halted and are then backing - you can work some on backing softly when ground driving.
Ground-driving in the arena can be fun - you do all sorts of figures with changes of direction and pace, and can also incorporate ground poles. And one way I've found ground-driving very useful is to introduce a horse to new sights and sounds, and to the trails. Maisie and I spent a lot of time getting used to things while ground-driving - it was a low-stress and easy way to have new experiences. This worked particularly well for Maisie as she was one of those horses who was easier to deal with on the ground than under saddle if things got worrisome.