No.

Quadratic Functions

https://en.wikipedia.org/wiki/Quadratic_function

The first two links are good, because they’re about quadratic functions, not the quadratic equation, which was your earlier link. But, this is just semantics now. PeteHski’s original objection to my use of the term quadratic was because of the absence of the linear term in aerodynamic drag. We all agree that the term is not required in a quadratic function; we’ve just stated it differently.

on edit: yep, you stated the same while I was (slowly) typing, so we’re all good!

on edit again: okay, now you deleted all that. I can’t keep up…

I didn’t say you were wrong.

His mistake was thinking the coefficients had to be nonzero.

(The quadratic equation is about finding roots of quadratic functions.)

Not getting dropped is #1 priority. Once that happens you are alone battling the wind. That's even less efficient than pedalling down hill. But if that is what it takes to keep up, that's what you do. Riding alone, pedalling hard down hill makes little sense. Better spend your energy going up and coast or soft pedal down.

Yeah, that's what threw me a little. But anyway we all agree aero drag is directly proportional to speed squared and it is a very simple quadratic function.

You'll never ride away from them with a 42x18. They're rocking 52 or 53 x 11. At 30 mph you'd be thrashing away at 160 rpm, bouncing all over the place and wasting tons of energy. You're leaving a ginormous hole in the air. They can tuck into that and roll along at a nice, easy 80 rpm - barely ticking over. If they spin up to 90 rpm, they're going almost 35 mph, and you're OTB and flailing like mad, unable to catch up. Weight gives you some advantage, but you're giving up all that advantage and more by sitting up and by trying to push a 42x18.

Years ago, I was riding with a smallish woman. She as not only no more than 5'3", she was also thin, so MAYBE 110lbs soaking wet. I'd just pulled us along Portola, so when we hit Alpine, she took the lead, and was pedaling away for dear life, while I was coasting, and having to brake a lot so as not to roll over her. After about 30 seconds of this, I pulled around her and said, "Here, let me..." and pulled all the way to Santa Cruz Avenue, at a speed she'd never have managed on her own.. I let her pull us along the Alameda, since that's flat/rolling.

Yeah im talking about on a road bike, Ive attacked down alpine thinking I would smoke the group with my weight but always get caught. Trying to keep up on alpine on the SS is very painful, mostly spurts of 160+ RPM between trying to tuck in

I ride a route with 3000 feet of climbing over 22 miles that's about 90% climbing, so on the descent, there's an equal amount of descending. The steepest grade is only about 6%, but with some tail wind I can sometimes spin up to around 120 rpm and 44 mph with my 48/10 top gear that's the same as a traditional 53/11. I coast briefly if the grade takes me into the mid to upper 30's. Except for the steepest grades, I'm pedaling at 90-100 rpm and only applying a modest torque which is soft pedaling. My heart rate stays well under 150 bpm, so I'm not working very hard on this very long descent, but I'm going significanty faster than I would by coasting. After 22 miles of climbing, I want some easier riding on the way down.

I played around a little on Bikecalculator.com. Unfortunately, although it takes rider weight as a parameter, it doesn't have rider height.

Alpine is about a -2% gradient. For you, at 260, essentially riding on the tops, going 30 mph would take almost 400w. A 160 lb rider in the drops would require a little over 400 w. BUT, if you're ahead of them, they might only have to put out 70% of that, which is only 280w. So, you're putting out power you probably can't manage for more than a couple minutes, max, while if they're sitting in the big hole you punch through the air, they're putting out power they might be able to manage for an hour or more. If you watch attacks in pro cycling, or even amateur stuff, almost nobody attacks from the front. The riders behind just accelerate to get back into the slipstream and they're ALWAYS doing less work. Attacks can work if you pass the guys in front already going A LOT faster than they are. So, you MIGHT drop them if you 1) start from the back of the pack, 2) pass the front of the group doing 30+ when they're going 25, and 3) are in the drops. That 400w that only gets you 30 mph when you're sitting up will get you 35 mph in the drops.

But, you know, if you're already running on the edge of the red just sticking with them, you'll never drop them. They're that much stronger.

EDIT: Credit for my understanding of this comes from watching the NorCal Cycling channel on YouTube. He does a really good job of explaining this stuff, using his own and others race footage. And the videos are fun to watch!

Dropping someone on a shallow non-technical descent is virtually impossible unless you have a massive power advantage. Pros never even think about attempting that sort of move. It's just stupid.

Well its only on the slow days that I am strong enough to attack, and its rare for someone to follow. They just watch me blow myself up off the front for a few minutes max until im caught by the wednesday social ride and then often am gassed and dropped altogether.

But do your brakes work?

when riding with a group? of course

On my regular 22 mile descent yesterday, a group of 5 young and serious looking riders passed me quickly, so I latched on, staying 4-6 feet behind the last rider. I had no problem keeping up with this group who were all probably 40 years younger. You don't need to stay very close to benefit from the draft. I even managed to stay in contact along a short stretch where the slope went up.

Exactly. It's a piece of cake to sit behind a group on an easy descent or even flat terrain. The guy up front is saving you roughly 30% in terms of power.