After spending too much time thinking about the meaning of cadence, I went off on a tangent and decided to do way too much math and science.

To do better math of course, I need better inputs. Since I don't have a power meter, I have been estimating power based on weight, friction, acceleration and drag. This are all reasonably easy things to estimate with some certainty and good data is available to at least get ballpark numbers. When I'm alone on my road bike.

Lately the only time I have to get out, I am towing my son in his trailer and of course its heavy, but does anyone have any reasonable idea what CdA I might have with a bike trailer?

Aside form the answer of buy a power meter. I suppose I could also learn some CFD, as I've already gone a bit overboard in my analysis...

Roughly, it's already behind you in your slipstream. The CdA of the trailer isn't going be nearly as insignificant as the weight and Crr.It's probably not negligible, but it certainly won't be the biggest factor in the increased power needed.

I'd just take whatever you estimate your power to be without a trailer and multiply it by 1.6. If that doesn't make you happy, try 1.9 or 1.7 or some other number.

Look up Cd for a rectangular box at Re~10^5, estimate A for your trailer, reduce CdA for the trailer by about 25-30% for being in your draft and add to your CdA. Plug the inputs into analyticcyling.com to get speed as a function of power or power as a function of speed.

Wonder if you could borrow/rent a power meter, take some measurements and calculate the drag...

Yeah, I started with this. It's probably close enough.

OK, Perhaps I shall calculate the trailer as a Borg Cube.

My daughter is now 29, I used to pull her in a trail over 25 years ago and had the same questions. Back then, I found some research around motorcycle trailers that I remember as something like the frontal area of narrow trailer resulted in a CdA of something like .4 but the same volume trailer in the shape of a cube was more like 2.0!

I pulled Lauren in a Winchester trailer (I think later bought by Burley) that was more like a cube than a narrow cargo style trailer. It was like pulling a parachute but the good news is never really went very fast with her in it - mostly on paved trails - so the aerodynamic penalty really didn't kick in that much.

I would definitely err on the side of cube shaped calculations! But, if you are any doing any hilly riding, you can also have fun changing rider weight to add child + trailer -- or in my case back then child + friend (or occasionally dog) + toys and calculate your wattage to do 4 mph up a hill...

This inline 2-seater is probably pretty slippery insofar as child trailers go!

Yeah, the cube seems a bit much. Poking in random numbers in Matlab, I seem to get similar average power values at ~CdA of 1 vs CdA ~.35 for similar perceived effort including weight. It is fun to see ~300-500 watts going up hill (large overpass), I certainly can't keep that up long. Good things hills around here are short. I usually use a mountain bike for trailer hauling but put it on my road bike the other day. Average speed for some moderate perceived effort went from ~18 to ~13-14.

I guess I'll keep collecting data to get a larger data set.

I'd imagine, looks like fun, maybe less so with the sidecar...

You’d think that, but it’s not. It’s like towing a parachute. The weight becomes a factor as it increases (ie, the passengers get bigger), and especially up hills obviously, but the Drag factor is significant. I speak as the parent of twins who towed them around in a trailer for the first 3.5 years of their lIves.

I used to do radar detection modeling without the benefit of "appropriate" finite element E&M codes. I was able to find a little actual data characterizing the objects I wanted to detect and to align them with known models of simple shapes, which could then be aligned to laboratory test objects. It was never "as good" as real-world data taken based on complex shapes, but real world data showed amazing sensitivity to rotation of the target object. A Borg cube versus a plain glass cube might give you much more uncertainty than can be handled. My modeling did allow me to come up with generic estimates of collision avoidance

I played with such cycle propulsion calculations without a trailer in the model using analyticcycling, and I think it's really good using objects that are in its library. Perhaps you can find a hint at CdA from a company that makes trailers, and then model that with a known simple geometric object. You don't need a military-grade result that can substitute for a true physical test.

One conclusion I'd probably draw is that if I was to face a 500 W hill load on a daily basis, I'd want to work on my gear ratios to make sure my legs have every opportunity to pull that load as I work into the cycling season! If you're climbing at walking pace, who cares, as long as you don't fall over due to low-speed instability. And even if you don't climb in Zone 5 with your kids in tow, you're still building the muscle needed to inch up your dh/dt! Sooner or later they'll be saying "wow, daddy, we're going faster!"

Try this:
https://www.recumbents.com/WISIL/tetz/cda/coastdown.pdf