Reaction Times

[Crabby_Bob]

[...]

1) Some of the early posts ignored drag effects which was noted by someone who also commented that drag is proportional to velocity squared. Actually, at low speeds in low viscosity fluids (think baseballs/softballs in air), drag is pretty well modeled as proportional to velocity (vs. velocity squared) so the math isn’t too hard.
2) All else being equal, a softball experiences more drag than a baseball at any given velocity because of its larger cross sectional area.
3) Drag is not the same as deceleration. Drag is a force, and the deceleration caused by that force depends on the mass of the object in question. Since softballs have more mass than baseballs, a softball will decelerate less than a baseball when subjected to the same drag force for the same period of time.
4) Netting out the effects of cross sectional area and mass differences, a softball will decelerate about 25% more than a baseball if both start at the same velocity and travel for an equal time. In other words, the difference in cross sectional area has more impact than the difference in mass between the two balls.

[...]

Apologies for straying from the thread subject. The last time I looked at this, I concluded that a softball, being less dense than a baseball, is more susceptible to aerodynamic forces than a baseball. Makes sense if you think about it. What would happen to an iron shot the size of a baseball? How about a tennis ball? a beach-ball?

Something else: calculate the rotational moment of inertia of a baseball and a softball of uniform density. You'll find for the softball it's about 2.4 times that of a baseball. This means the softball is much harder to spin up. What's the limit of human ability? i.e., is the human torque limited, or angular acceleration limited? I'll bet it's dependent on the object. Otherwise, I haven't the foggiest idea.

[hit4power]

Apologies for straying from the thread subject. The last time I looked at this, I concluded that a softball, being less dense than a baseball, is more susceptible to aerodynamic forces than a baseball

No apology needed, we hijack threads all the time on here, and by now, I think there are only three of us still reading this thread anyway.

All the discussion so far has ignored the fact that both baseballs and softballs have seams and are spinning so in the real world they behave quite differently than in the simple models we've been discussing. The actual forces they are subject to arising from the interaction between surface of the ball and the air are very complex. When you say that a softball is less dense than a baseball and therefore more impacted by "aerodynamic" forces, I agree, although I would state it as because a softball has a (much) larger cross sectional area and (slightly) more mass than a baseball (and therefore is less dense) it will be more affected (experience larger accelerations/decelerations) than a baseball by the same level of aerodynamic force (drag, for example). My only point being that density is the result of the physical properties that actually matter (area and mass) when comtemplating the ball's reaction to aerodynamic forces.

[PDad]

Something else: calculate the rotational moment of inertia of a baseball and a softball of uniform density. You'll find for the softball it's about 2.4 times that of a baseball. This means the softball is much harder to spin up. What's the limit of human ability? i.e., is the human torque limited, or angular acceleration limited? I'll bet it's dependent on the object. Otherwise, I haven't the foggiest idea.

I don't think the relative MOIs are much of an issue since the values are so small. Example: a 5oz object is 2.5 times as heavy as a 2oz object, but I doubt there would be a discernable difference in how quickly you could lift them since the loads are so light. This would discount human torque as a limiting factor for imparting spin.

I think the different throwing motions, overhand vs. underhand, would be the biggest factor in how much spin could be imparted (angular acceleration).

I'm not sure how much impact the different sizes of the balls would be on either throwing motion. Once they got used to the different sized balls, I would expect they could generate the same amount of spin (RPMs) with either ball since the motion that produces the spin is rotational (i.e. wrist snap) rather than linear (e.g. rolling a ball).

[anonlooker]

I don't remember this aspect being covered earlier... and with all the mathematics wizards in on this...

what difference will the change from 40' to 43' make. It will obviously increase time to track the ball, but by how much, and will be as significant as many suggested when the distance change was announced?

[PDad]

MPH / Ft/Sec / # Feet / Secs From Release to Front of Plate
Fastpitch
70 101.1 36 0.356
69 99.7 36 0.361
68 98.2 36 0.367
67 96.8 36 0.372
66 95.3 36 0.378
65 93.9 36 0.383
62 89.6 36 0.402
60 86.7 36 0.415

Formulas:
Miles per hour converted to feet per second: mph*5200/3600
# Feet MLB: 60.6 - 5 foot stride to release point, - 1foot to front of plate # Feet Fastpitch: 43 - 6 foot stride - 1 foot to front of plate
Seconds to Plate: # Feet / Ft per Second

FYI - There are 5,280 feet per mile. All your ft/sec are low which in turn causes your reaction times to be high.

I was wondering how you came up with 86.7 ft/sec instead of 88 for 60 mph...

[PDad]

I don't remember this aspect being covered earlier... and with all the mathematics wizards in on this...

what difference will the change from 40' to 43' make. It will obviously increase time to track the ball, but by how much, and will be as significant as many suggested when the distance change was announced?

Okay, but I'm stipulating the following:
- MPH is the average speed over the travel distance (i.e. includes drag from air resistance).
- Travel distance = full pitching distance minus 7 feet (stride & plate).
- Reaction time = travel time minus .15 seconds to execute swing.

Code: Select all

                 40'    40'     43'    43'   Delta  Delta   
MPH    Ft/Sec  Travel  React  Travel  React  Secs    Pct.   
 55     80.667    33    .259     36    .296   .037   14.35%   
 56     82.133    33    .252     36    .288   .037   14.51%   
 57     83.600    33    .245     36    .281   .036   14.66%   
 58     85.067    33    .238     36    .273   .035   14.82%   
 59     86.533    33    .231     36    .266   .035   14.99%   
 60     88.000    33    .225     36    .259   .034   15.15%   
 61     89.467    33    .219     36    .252   .034   15.32%   
 62     90.933    33    .213     36    .246   .033   15.50%   
 63     92.400    33    .207     36    .240   .032   15.67%   
 64     93.867    33    .202     36    .234   .032   15.86%   
 65     95.333    33    .196     36    .228   .031   16.04%   
 66     96.800    33    .191     36    .222   .031   16.23%   
 67     98.267    33    .186     36    .216   .031   16.43%   


[Tumblebug]

I started to get into this but I kept getting sidetracked with tangential subjects and results that interested me more. I gave up to attend to my normal life, such as it is. I think you could spend a lifetime in just the math of the original question and the tangential subjects that follow. That is all, carry on.

[PDad]

I started to get into this but I kept getting sidetracked with tangential subjects and results that interested me more. I gave up to attend to my normal life, such as it is. I think you could spend a lifetime in just the math of the original question and the tangential subjects that follow. That is all, carry on.

You'e excused. We'd much rather have you focus on getting the NanoTek FP into production and figuring out how to efficiently produce a consistent drop-weight across all the lengths of each bat model.

[anonlooker]

I don't remember this aspect being covered earlier... and with all the mathematics wizards in on this...

what difference will the change from 40' to 43' make. It will obviously increase time to track the ball, but by how much, and will be as significant as many suggested when the distance change was announced?

Okay, but I'm stipulating the following:
- MPH is the average speed over the travel distance (i.e. includes drag from air resistance).
- Travel distance = full pitching distance minus 7 feet (stride & plate).
- Reaction time = travel time minus .15 seconds to execute swing.

Code: Select all

                 40'    40'     43'    43'   Delta  Delta   
MPH    Ft/Sec  Travel  React  Travel  React  Secs    Pct.   
 55     80.667    33    .259     36    .296   .037   14.35%   
 56     82.133    33    .252     36    .288   .037   14.51%   
 57     83.600    33    .245     36    .281   .036   14.66%   
 58     85.067    33    .238     36    .273   .035   14.82%   
 59     86.533    33    .231     36    .266   .035   14.99%   
 60     88.000    33    .225     36    .259   .034   15.15%   
 61     89.467    33    .219     36    .252   .034   15.32%   
 62     90.933    33    .213     36    .246   .033   15.50%   
 63     92.400    33    .207     36    .240   .032   15.67%   
 64     93.867    33    .202     36    .234   .032   15.86%   
 65     95.333    33    .196     36    .228   .031   16.04%   
 66     96.800    33    .191     36    .222   .031   16.23%   
 67     98.267    33    .186     36    .216   .031   16.43%   


So in looking over this chart, it appears that a 60mph fastball at 43' gives the hitter the same reaction time as a 55mph fastball at 40'... effectively turning a 60mph pitcher into a 55mph pitcher???