Here in the south of England on calcareous chalk and limestone grassland, and there is a lot of that in Dorset, we find the stripe winged grasshopper (Stenobothrus lineatus). They have a preference for shorter grass and for southerly facing slopes. They have white and black stripes on the outside of the wings but they are hard to tell apart from the common green grasshopper which is similar. In any event, adults of the same species can vary!
Grasshoppers are tricky chaps to tie down unless you have an experienced eye as they can fly away from you (yes, they fly in short bursts rather than hop) as they are pretty sensitive to movement. If you have good hearing you may be able to identify them by sound. All grasshopper make differing sound patterns (stridulation), it is a bit like the concept of Morse code, and that is the best way to identify them but it takes time and effort to understand and match the patterns of sound to the species of grasshopper. If your hearing is past its best then a bat detector can make the sound audible at a lower frequency, as a crackle, and you can then home in on them. If you are really careful you can strike lucky, especially if the sun goes behind a cloud at the right moment!
Often in the company of meadow grasshoppers and common field grasshoppers just to make things more challenging but neither of those species have green along the back.