What is this formula being used to calculate drag force?

[grandpa2390]

A good place to look for some information about drag on a sphere is on the NASA website https://www.grc.nasa.gov/www/k-12/airplane/dragsphere.html. NASA does so much work in this area that they are a "must-know" resource. Other NASA drag coefficient information is at https://www.grc.nasa.gov/www/k-12/airplane/dragco.html .

but a baseball isn't a sphere. it has a rough surface that gives it a better drag over a sphere :)

 

[FactChecker]

but a baseball isn't a sphere. it has a rough surface that gives it a better drag over a sphere :)

They have a page just for baseballs. https://www.grc.nasa.gov/www/k-12/baseball/index.html

 

[haruspex]

I meant that the wind is horizontal, not the relative motion.

Yes, I thought that was what you meant, so I disagree with your statement.

That is because you are expending force and energy to keep going straight on the road, so in effect you are steering into the wind. A thrown ball just goes with a cross wind. The same is true of an airplane that is not "crabbed" into the wind

In those cases you cite, the projectile has, more or less, acquired the same lateral velocity as the wind, so there effectively is no wind.
For the bicycle, one's intuition may be that the lateral static friction from the wheels will counter the crosswind. Indeed, at low speed, with a linear drag, this is correct; the crosswind should not slow you at all. It is the quadratic drag which makes crosswinds a problem for cyclists.

Have you looked through equations I posted? Can you find a flaw there?

 

[FactChecker]

For the bicycle, one's intuition may be that the lateral static friction from the wheels will counter the crosswind.

In a crosswind, the bike will lean into the wind in a way that would otherwise cause it to turn in the direction of the wind. That turn is opposed by the wind and there is an associated increase in work required to maintain a steady speed in a straight line.

Indeed, at low speed, with a linear drag, this is correct; the crosswind should not slow you at all. It is the quadratic drag which makes crosswinds a problem for cyclists.

I have always considered drag to be proportional to the velocity squared, not linear.

Have you looked through equations I posted? Can you find a flaw there?

I see your point. I can't see an error.

 

[haruspex]

the bike will lean into the wind

Yes.

That turn

What turn? The bike still goes in a straight line, and the front wheel still points straight ahead.
The lateral static friction at the road contact counters the lateral component of the drag, while the net torque from those two is balanced by the torque from the gravitation/normal force pair.

I downloaded the NASA baseball applet, but I can't get it to work. It puts up a page with a banner naming the applet etc., but the rest of the page is blank. Tried it with both Google Chrome and IE.

 

[FactChecker]

@haruspex , I stand corrected. After looking at your equations, I think that you are correct that a headwind should decrease the maximum height of the ball's trajectory (I still need to get it clear in my mind.) I think that is the main issue of relevance to this thread.

The following issues are side issues to the OP and I am afraid that we may be hijacking this thread. But here are some final thoughts on my part.

Yes.

What turn? The bike still goes in a straight line, and the front wheel still points straight ahead.

The steering geometry of a bicycle, and much more so of a motorcycle, includes a head tube angle, rake and trail that applies a torque to the front wheel when it is leaned into the wind.

The lateral static friction at the road contact counters the lateral component of the drag, while the net torque from those two is balanced by the torque from the gravitation/normal force pair.

A rolling tire does not have the usual lateral static friction. Because of tread distortion, the tire can move laterally as long as it is rolling. In order to travel in a straight line without lateral movement of the vehicle, a rolling tire must point to oppose the lateral movement.

I downloaded the NASA baseball applet, but I can't get it to work. It puts up a page with a banner naming the applet etc., but the rest of the page is blank. Tried it with both Google Chrome and IE.

I have never used it. I see that they say it is a beta test version and that PC security software may stop it from running. I don't really know anything about it.

 

[haruspex]

The steering geometry of a bicycle, and much more so of a motorcycle, includes a head tube angle, rake and trail that applies a torque to the front wheel when it is leaned into the wind.

Sure, but the cyclist applies a static torque to the handlebars to stop the wheel turning. Muscle dynamics apart, no work done.

A rolling tire does not have the usual lateral static friction. Because of tread distortion, the tire can move laterally as long as it is rolling. In order to travel in a straight line without lateral movement of the vehicle, a rolling tire must point to oppose the lateral movement.

True, that will add a bit more to the load on the cyclist. But I maintain that the crosswind would still slow the cyclist even if that tendency to creep were balanced by, e.g., camber.
Indeed, this "creep load" would also arise on road that is cambered more than required for the cyclist's speed and no crosswind. Can't say I've ever noticed that making for harder work.