I also fucked up my back with heavy weighted sit ups so I don't wanna risk it anymore. One of the best exercises in my opinion are heavy carries with db's, kb's or even normal farmers handles if available. You can a lot of different variations. Like heavy load in both hands. Heavy load in one hand on the side and the other weight over head. Both hands overhead etc. Just grab some weights and walk... simple but very effective and imho a lot more "functional" than doing leg raises or decline situps...
Functional? Functional if you training to be a strongman or to carry heavy things, sure. Functional if your goal is to run fast? Not so much. Core strength in sprinting and jumping is about being stiff to allow you to transfer power - watch Justin Gatlin torso stay extremely stiff and still while his legs produce tons of power... Heavy farmers walks have the weight in your hands - this doesn't make sense for sprinters.
my n=1 is that heavy weighted decline situps fuck up my back if i do them too frequently or too intensely. much prefer toes-to-bar; ab wheel rollouts also good.
Obviously LBSS makes a point. We are all N=1. There is no must do exercise. If an exercise causes injury to your body you don't need to do it. There are great athletes who don't do lots of exercises. As blasphemous as it sounds you can even become a great athlete with squats!
However, there are a few exercises that do past the "ability test". What I mean by that is not that you must use it as a training tool but that in my observation of sprinters where N == A LOT - I have seen very very very few fast athletes who cannot execute it well if given time to acclimate to it. Obviously this is a continuum. Some sprinters can bench press a great deal but I have seen many sprinters who can't bench press much at all even when given time to learn the exercise. For squats this is less true. Two of the exercises I find to be by far the most correlated with sprinting speed are:
1) Heavy overhead backwards shot tosses
2) Weighted decline situps
I don't mean all sprinters train with these exercises. But show me a sprinter who runs 10.5 and is given a mens shot put and shown how to throw it backwards and cannot throw it 15 yards and I will be shocked. I haven't seen one. Dan Pfaff goes further with this and claims it actually is extremely strongly correlated in female** sprinters and he gives specific speed and shot throw distance relationships.
For decline situps I am talking about the following exercise. Grab a 45lb barbell. Hold it behind your back like a backsquat*. Get in a 45 degree decline bench and keep your abs and back tight and lower controlled till you touch your upper back only to the bench and rise back up to sitting. Flex hip flexors to bring body up. Yes it is an ab and hip flexor exercise. They are a team! Most people cannot do even one rep. Almost all good sprinters can bang out 5-10 of these the first time they learn it.
* It's important that you hold the bar like this. Not just cause it makes it harder but because it saves your back. When you hold weight across your chest its natural to bend at the spine to bring your upper torso up to your legs and fold your body over. This is what messes up your back. Having the bar in back squat position doesn't take the back out of it but IMO it makes it obvious when failure should be (the point where you can't do more reps without wrenching your back).
** While Dan Pfaffs claims seem almost too specific it does not surprise me that he finds a better relationship for females. Men often ruin exercises because they are strong. There are probably men whose massive upper body strength allows them to throw a shot far behind their head despite no hip strength which probably ruins this relationship. I haven't trained that many women but it really is the key to understanding the relationship between proper strength training and performance.
*** Again, not saying that an exercise is a must do - just adding that there are some exercises that are compelling to try because of their association with performance. Could be a chicken and egg argument - not proof of anything just food for thought. Agree with LBSS that toes to bar is a good ab exercise, not a huge proponent of ab wheel. I would rather have an athlete do toes to bar, weighted and unweighted leg raises on decline bench, and extended push ups...