While drawing diagrams to calculate it would be fun, have you considered comparing your heart rate with and without the stroller?
That would be a much more reliable than trying to estimate the increased energy requirements. Here's why:
- We would need to calculate the friction the stroller has with the ground, which depends both on its weight (with or without a baby) and the amount of contact surface with the ground. The latter may vary if you have 3 or 4 wheels, high profile wheels or not etc.
- We would need to calculate the increase in your frontal surface, so we can estimate the air resistance. While most models are quite aerodynamic, so the baby would be dry, I can't even make ballpark estimations about what your total change in air resistance will be.
- The energy transfer of you pushing and the stroller rolling forward. Ideally you would be pushing straight ahead, so all your energy is converted into a forward rolling motion (assuming there are no moments that require you to push under an angle). Either way, remember you're running, you have better things to do than pushing under some weird angle and making sure the baby is safe! So we have no idea what the energy loss is going to be here, perhaps you lean too much on the stroller (increasing the friction) or you're slightly lifting it (making your own steps heavier).
Regardless of all my points, what value does the answer have?
- If you want to burn more calories, you can also run longer or faster, no need to push a stroller.
- Need to take baby out for a ride and worried of all the extra work, simply run slower so you'll burn the same net amount of calories.
So you're still convinced you need to push a stroller and run at the same time? Like I said, simply compare your rate heart with or without on several runs (science requires multiple samples!) and see how the compare. To make sure you're not cheating, track your speed using GPS or an accelerometer and you get an idea of what the influence of the stroller is. Estimating it however, surely is not the way to go.