Holy cow. There are easier (faster) ways to do comparisons like that.
Define “much”. If you’re a casual rider who doesn’t race, no it’s not much. If you’re a performance oriented cyclist or race, every watt matters.
If that’s the case, and the time saving was ~3mins over 100km, then for someone like me (~70kg, 250 ftp, old) who:
- (a) never averages more than 30km/hr on my home constantly up/down rolling terrain, ie. <= 2/3 of the test speed, and
- (b) on solo easy z2 type rides may be as slow as ~1/2 of that tested speed
…then we are likely into the realm of the aero benefits not really being discernible, as suggested earlier by the OP with his speeds. Still some benefit, but seriously tapering off, and while measurable if you could instrument for it, not really something you’d be “aware of” in any sense.
The slower you are, the more time you save.
At 1/2 the speed I have 1/4 of the aero benefits?
The effect of aero savings on time savings is almost exactly the same proportion across all speeds, so if you save 1% in time at high speed you’ll save almost exactly 1% in time at low speed. The slower you are, the more time you spend on the road so the slower you are, the more time you save.
Why is that the case if aero drag is proportional to velocity squared?
Because time savings isn’t the same as aero drag. Do the math: plug in some values and you’ll see that time savings from a decrease in CdA is very close to proportional no matter your speed. But you spend more time on the road when you’re slow, so the savings are larger when you’re slower.
This user name says it all - even better if it is in fact Robert Chung himself (if so, thank you for popping in/out).
Can you lay out an example?
I’m not sure the point of your post. Nobody is suggesting that everybody needs aero everywhere and all the time.
If a rider just rides around casually, smells the roses, stops for coffee, etc, etc. then they certainly don’t need spendy aero wheels or an aero frame nor a $15,000 super bike.
Need and want though are often at odds when buying gear. 
As I posted above, buying aero wheels, jersey, and helmet helped bag a bunch of KOMs and those extra 30-40 watts really helped on group rides when the group really got moving. Did it help when I was sitting in the group and they were just cruising at an easy pace? No.
But other than those situations, nobody cares if you are riding at 1 mph faster when doing your training rides. Who cares if you arrive home a minute sooner?
The point was an attempt to map the Tour measured findings to my own situation, to gauge the benefit I’d enjoy and have a stab at the “discernibility” of those benefits.
The Man has entered the chat.
As Dr. Chung said, you’d save more time.
But is that time important to you - probably not.
For amateurs, aero shines at the pinch points - going for a KOM, taking a pull on the group ride, etc. That could be just a few minutes out of a ride or out of the week.
Do we discern going an extra 1 mph? Not really. Does it matter? It depends.
Of course, but in my day job I’m a professor so I like the students to do the numerical examples by themselves (if they can). So before I lay out a numerical example, let’s try this:
You know that aero drag increases with the square of velocity (and the power to overcome that drag increases with the cube of velocity). IOW, a 1% increase in velocity means a 1.01^2 increase in aero drag or a 1.01^3 increase in power to overcome that. It doesn’t matter whether that 1% increase in velocity is from a base of 45 km/h or 30 km/h; the percentage increase in drag or power doesn’t depend on the starting speed. You can reverse this, and see that a fixed percentage decrease in drag is going to result in an fixed percentage increase in speed, no matter what the starting speed, whether that speed is fast or slow. So if the speed changes by a fixed percentage no matter speed, the time saved also changes by a fixed percentage no matter the speed. But at slower speeds, the elapsed time is longer so the time savings in seconds (rather than a percentage) is greater.
If you still are having trouble with this, I can do a numerical example–but I like it when the students can understand the logic even more than when they can do the calculations.
Yup. We treat these things as if we were all doing TTs, but in mass-start racing there are a series of crises, or pinch points. If you survive a crisis, you live for a little while longer until there’s another crisis. Lather, rinse, repeat. If you get dropped, the gap can balloon out to minutes; if you survive, you may be squeezed off the next time. But the aero bike lets you stick around for one more crisis than otherwise.
If you never race, or if you’re anti-social and never ride with a group of friends, maybe aero won’t matter to you because there are no pinch points.
Thanks.
Assuming(?) this numeric example I picked up from r/cycling is correct:
If a pro tour rider who can do 400 watts on a 25mile course saves 16 seconds from an aerodynamic improvement, a coffee ride guy who does 200 watts will save 20 seconds over the same course.
If that seems wrong to you, note that the 400watt rider has saved 16 seconds out of 55 minutes and 27 second
The 200 watt rider has saved 20 seconds out of 1 hour 11 minutes and 12 seconds.
So the 400 watt rider has saved a better % of time, reflecting that his drag reduction was bigger due to higher speed. But only a little bit!
…then my calculator suggests the pro-rider gains a ~0.48% time improvement, while the slow rider enjoys a ~0.468% improvement, so a slightly smaller percentage of time saved, but this slightly smaller percentage applied to a materially longer duration equates to more actual time saved for the slow rider (20s vs 16s in that example).
Bearing in mind how, as you state, “aero drag increases with the square of velocity (and the power to overcome that drag increases with the cube of velocity)”, the modest differences in the percentage time improvements between the 400w rider (~0.48%) and 200 w rider (~0.468%) seem unintuitive, amounting to just a ~2.7% additional proportional benefit for the pro vs slow rider…
Q: What is it (in the physics / the calcs) that causes that “flattening”, ie. causes the percentage time benefits enjoyed by the 400w pro rider and the 200w slow rider to be so close, despite the square and cube relationships involved?
There’s an aero component in the power-drag equation and a rolling resistance part. You know that the aero drag component varies with the square of speed (the power to overcome the aero drag varies with the cube of speed) but the rolling drag is constant with speed (the power to over the rolling drag varies linearly with speed). But the rolling resistance part tends to be small compared to the aero part. So that’s why I wrote the percentage time savings “is almost exactly” the same no matter the speed instead of “exactly” the same. The rolling resistance part screws up the exactness part. But we were talking about aero bikes so I was trying not to get into the rolling resistance part.
But this would mean that there are people out there selling us stuff we don’t need…their whole careers dedicated to marketing products regardless of their value…
Pfft, that could never happen!
Everything is marketed to us.
It’s not some grand conspiracy that the bicycle industry comes out with new models every year. Nobody is twisting anyone’s arm to buy a new bike, new wheels, a new iphone, a new car, or anything else.