I recently did an interview with Richard Diaz for his Natural Running Network podcast. He began by asking me about efficiency in running, and I first gave an overview of the forces involved and how they break down into vertical and horizontal components.
After the interview, I thought about how difficult it is to explain this concept to someone without getting lost in all the different elements that come into play. Then it occurred to me that there's already an almost universally understood example of how changing the magnitude of our vertical and horizontal force components changes efficiency of movement. It's everyone's favorite smart phone game: Angry Birds.
Consider your typical Angry Bird scenario. There are some rather smug pigs arrayed along a field at varying distances from your slingshot. You pull the slingshot back, let it go, and your birds unleash their feathered fury.
Depending on which pig you want to hit and how far away they are, you have very limited options on how to get your bird to the target. There's only so much stretch allowed by the slingshot, which means there's a limit to the amount of force you can use. The birds all weigh the same, and their aerodynamic properties are similar (at least until you hit the screen again and activate their special powers). So there's only one thing you can do, which is to change the angle of your shot.
Now, let's think about what we're actually doing when we point the slingshot further upward or downward. We know we have a finite amount of force to use. If we point the slingshot straight up, all the force moves that way. If we point it straight ahead, all the force goes that way. This seems intuitive enough, but it's what happens as a result that really starts to illuminate the problem of efficiency in running.