Terminal Velocity ???

Is it a movie title, album title, video game, or a concept in physics? I checked The Encyclopedia Britannica where it was defined as, "the steady speed achieved by an object freely falling through a gas or liquid." What’s that supposed to mean? It has something to do with acceleration which the same encyclopedia defines as,"At the Earth's surface, the acceleration of gravity is about 9.8 metres (32 feet) per second per second. Thus, for every second an object is in free fall, its speed increases by about 9.8 metres per second." I think my head just expoded.

Well I seem to be okay "sort of" but that clears up nothing. I tried to figure it out. As luck would have it (after hanging on to them for years) I had throw out my college physics books a month ago. So I searched the Internet for the answer hoping to find the formulas to calculate acceleration and terminal velocity in air or a vacuum. What did I find? Garbage, pure garbage!

Why do I even care? Well last year I took my shot at reaching terminal velocity by launching my self down my cellar steps. I broke a couple of ribs in the process and missed three weeks of skiing because of my attempt at a "Darwin". Three weeks past that attempt my ribs (or something) still hurt but I went skiing anyway (why not I spent three hours shoveling snow so why not ski?). Ques. What did all this teach me? Ans. People publishing on the Internet know about as much about physics as I know about menstrual cramps and oh yeah, broken ribs REALLY HURT.

What bothers me about this? I am not against freedom of speech but if you are going to publish something on the Internet please be honest about your knowledge of the subject, or make it funny and let people know you are joking, or lie about it and admit you are, "Rosemary’s Baby."

I did however, find out that I could not have reached terminal velocity in a fall down my cellar steps. They aren’t high enough. How did I find this out? I found a table on Wendy’s "Darwinawards" that said I would have to free fall for 12 seconds and cover 1483 feet to achieve terminal velocity. The "Darwin's" chart follows:

Seconds
of Freefall		 Incremental
Distance (ft)		 Speed
(MPH)		 Cumulative
Distance (ft)
1 16 10.90 16
2 46 31.36 62
3 76 51.81 138
4 104 70.90 242
5 124 84.55 366
6 138 94.09 504
7 148 100.91 652
8 156 106.36 808
9 163 111.14 971
10 167 113.86 1138
11 171 116.59 1309
12 174 118.64 1483

I tried in vain to calculate these numbers. Lets see, the encyclopedia said acceleration was 32 feet per second per second so in an ideal world (that’s a way scientists have of discounting the realities of the world such as friction) the first second I would fall 32 feet. You can see from the first row in the blue table below I am already in trouble according to the pink "Darwin's" table. Things get worse as the second row states I would be going (32 + 32) 64 feet after two seconds, and the third row is even worse stating I would be going (32+32+32) 96 feet per second after three seconds. I am just an accelerating fool. The further I go down the chart the further from reality I get. Below is my pathetic attempt at calculating acceleration.

Darwin's Acceleration Numbers Ron's Acceleration Numbers?
Seconds
of Freefall		 Incremental
Distance (ft)		 Speed
(MPH)		 Cumulative
Distance (ft)		 Seconds
of Freefall		 Incremental
Distance		 Speed
(MPH)		 Cumulative
Distance
1 16 10.90 16 1 32 22 32
2 46 31.36 62 2 64 65 96
3 76 51.81 138 3 96 131 192
4 104 70.90 242 4 128 218 320
5 124 84.55 366 5 160 327 480
6 138 94.09 504 6 192 458 672
7 148 100.91 652 7 224 611 896
8 156 106.36 808 8 256 785 1152
9 163 111.14 971 9 288 982 1440
10 167 113.86 1138 10 320 1200 1760
11 171 116.59 1309 11 352 1440 2112
12 174 118.64 1483 12 384 1702 2496

As you can see my numbers are no where near the truth (Darwin's) so I tried another way. I have heard 32 feet per second per second defined as 32 feet per second squared. Lets look at those numbers.

Darwin's Acceleration Numbers Ron's Science Fiction #s
Seconds
of Freefall		 Incremental
Distance (ft)		 Speed
(MPH)		 Cumulative
Distance (ft)		 Seconds
of Freefall		 Incremental
Distance		 Speed
(MPH)		 Cumulative
Distance
1 16 10.90 16 1 32 22 32
2 46 31.36 62 2 128 109 160
3 76 51.81 138 3 288 305 448
4 104 70.90 242 4 512 655 960
5 124 84.55 366 5 800 1200 1760
6 138 94.09 504 6 1152 1985 2912
7 148 100.91 652 7 1568 3055 4480
8 156 106.36 808 8 2048 4451 6528
9 163 111.14 971 9 2592 6218 9120
10 167 113.86 1138 10 3200 11040 16192
11 171 116.59 1309 11 3872 11040 16192
12 174 118.64 1483 12 4608 14182 20800

God they’re even worse than my previous attempt. What’s going on here? Am I a total idiot or what? Let’s stick with “Darwin's” numbers. It seems the more I try the further from the truth I get, so much for perseverance. Okay so what’s the point? I have far too much time on my hands since the end of ski season.

I have received some help with my delema. A fellow by the name of John e-mailed me with this explanation. “The mistake you are making is that speed at a particular time is at that instant only so….After the first second you would be falling at 32 feet per second but at time zero you were not be moving (much!) so the average speed would be (0+32)/2=16 feet per second average velocity for that first second so 16 feet are covered.” Wow! John went on to say,”In the 2nd second speed goes from 32 to 64 feet per second average. (32+64)/2=48 feet per second. This is different from Darwin’s numbers because we are not considering air resistance. (which is a lot more difficult to calculate) etc. “You get the idea?”

Well John I think I do. If I get your jist discounting air resistance would give us:

Ron's Latest Science Fiction
Seconds
of Freefall		 Incremental
Distance (ft)		 Speed
(MPH)		 Cumulative
Distance (ft)
1 16 10.90 16
2 48 32.7 64
3 80 54.5 144
4 112 76.4 256
5 144 98.2 400
6 176 120.0 576
7 208 141.8 784
8 20 163.6 1024
9 272 185.5 1296
10 304 207.3 1600
11 336 229.1 1936
12 368 250.9 2304

What's the latest table mean? Darwin's table still rules.

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