I've always had a pet peeve on this topic when I hear people claim that you should run so that your body does not "bounce" (i.e. you center of mass (CM) does not oscillate up and down much). It's a pet peeve because that assumption is generally wrong. I was motivated to write this seeing a new study on the topic discussed by Alex Hutchinson on his blog.
This is not a running-specific oversight, but a general issue when people attempt to make biomechanical insights without the proper training in biomechanical analysis.
You focus on the benefit of the output (moving forward), but you are forgetting the cost on the input (human body muscle demand).
1. In cycling, you do NOT necessarily want to push tangential to the crank arm.
2. In running, you do NOT necessarily want to push parallel to the ground (after accounting for body weight)
3. In wheelchair (WC) pushing (one area I studied in my phd thesis), you do NOT necessarily want to push tangential to the wheel.
In all 3 cases, yes you would want to push that way if all that mattered was optimizing mechanical output. But running / cycling / WC pushing economy is a balance between power output and the power input cost (muscle metabolic cost).
Gross Mechanical Efficiency ~ Power Output / Oxygen Input
You want to try to increase power output, but only if the load on the muscles (which relates to calories burned and oxygen consumed during aerobic exercise), does not.
An example of this is shown below, taken from one of my wheelchair studies. We are looking at how varying the angle you push on the wheel of a wheelchair affects the mechanical loading (moments, or torques) of the elbow and shoulder joints. At all angles, the tangential (propulsive) component is fixed, so the wheelchair movement is guaranteed, but the radial force component may vary.
A 90 degree force angle is purely tangential and what you would think is best. A lower degree requires a radial force component, and the force magnitude required overall increases. Wouldn't that increase mechanical demand of the upper extremity?
Not so fast. Notice the total moment demand is minimal at force angles less than 90 degrees in both subjects (S1 & S2). This is because while the overall force is greater, the upper arm and forearm have better leverage and effectively smaller moment arms and require less muscle activation to produce the force.
Same goes for cycling: You may think pushing tangential is best, but it really depends on the configuration of the femur and tibia relative to the pedal location. In some positions it probably makes sense to push tangential to the crank arm, but not always.
And in both cycling and wheelchair pushing, experimental evidence agrees: people don't push tangentially, for the reasons explained above.
Again, it's not just about force magnitude, but how that force passes through the segments of the body. What's easier, holding a bowling ball in your hand with your arm fully extended horizontally, or with your arm relaxed downward at your side? The latter is easier.
Back to Running
I have not personally studied running as much as wheelchair / cycling mechanics, but let's relate these concepts. "Ideally" you should push off your the ball of your back foot just enough to maintain your vertical position while moving horizontally. But what if your leg and body configuration really want you to push more vertically?
As shown above, the optimal force direction that gives the proper amount of horizontal acceleration but minimizes total muscular load may not be obvious. In running, your calves want to push you upwards, not just forwards, so it makes sense to me that vertical motion is just a side effect of the runner's force direction for optimal running economy.
Now, I imagine that if you have really great ankle dorsiflexion range of motion, then you can lean your body forward more before push off, and the force / stride angle can be reduced (and vertical motions reduced), and that may have the best running economy of all. But if you don't have that range of motion in your ankle, trying to run without oscillating will just make you less efficient.
Which of the following force angles do you think is most efficient? Both produce the same horizontal component (forward motion). The red is larger, but passes closer to the joints of the leg, and thus will have smaller moment arms. The green is smaller, but requires larger moment arms. Which requires more muscle activation?