“Tani Otoshi” is translated into “Valley Drop,” which is a sacrifice-type Judo takedown. The hand grip starts off quite similarly to Osoto Gari, with a collar and wrist grip. The difference is that, instead of just pushing them backwards, you also pull them up, ideally lifting them off their heels. Then, step in with your lead leg between their feet (in the squared-up position), with the other leg moving in a circle behind them to trip their leg while their momentum falls backwards.
You can either put your butt on the floor and use your collar grip, as well as your head, to push them falling backwards while extending your leg to trip them. The second method is to switch to a double underhook, grabbing your wrist over their waist (or holding onto their belt if in Gi), as soon as you are able to step your foot back and stand side by side with your partner. Pull them onto you, create a body lock, stick your body to theirs, and from there, do a sumo squat. Become a chair and push your head onto their chest or shoulder so they will fall backwards (onto the chair you created with your leg), effectively falling backward onto the mat.
Notice that you can switch to a single leg when attempting this takedown.
I had trouble attempting this takedown, as I’m afraid to hurt or injure my partner if I trip them incorrectly and twist their knee. I would go for the second variation of this, as it should work with both Gi and NoGi. I will look into this further.
