by Nikolai V. Shokhirev
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Measurement of Skin Smoothness; Safe Distance Measurements
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From a commercial: "This lotion makes your skin 30% smoother". This statement makes no sense unless some measurement procedure is defined. The procedure must meet the following requirements:
One can argue that this is not an exact science. OK, in this case you have no reason to use the term 30% (30% of what?).
It is possible to have a device that determines skin smoothness or roughness. But is it relevant? All this is about beauty, about human perception, how people look and feel. Ultimately this is about the quality of this lotion.
The procedure that is relevant to the subject might be like this: 1000 women used our lotion for a month. 30% of them feel that their skin remains the same, 10% think that their skin got worse and 60% feel that their skin became smoother. Let us check if this procedure meets the above requirements. One can deduce that
Now we can say that on average, three of five women that used the lotion experienced a positive effect. Proof: the ratio (Positive) : (All ) = (60) : (60+10+30) = (3) : (5). Of course you can do some other math in support of other statements, e.g. Positive and Neutral effect was observed in 90% of those tested.
Certainly this is not the only possible procedure, which is ok, as long as you described the used procedure.
Q: In my morning commute I use a road where all cars steadily move with the speed ~ 50 mph. I have to wait when the approaching car is far enough form me to make my turn safely (Fig.1). While I turn and accelerate my car the distance decreases to S (Fig.2). Obviously, for safety reason S must be greater than zero. On the other hand, large values of L are relatively rare, and therefore I will have to wait longer for a large L distance. The question is, "How to determine the minimal safe distance L?"
Fig.1. The initial distance L
Fig.2. The smallest distance S
A: Let us consider several approaches.
1. Theoretical method. The traffic moves steadily so the safe distance depends only on the dynamic properties of your car. In principle, knowing your car mass, engine power, etc. you can calculate the acceleration time to 50 mph. Using this time you can calculate L. Unfortunately the calculation is not easy and the uncertainty in dynamic characteristic is large.
2. Simple experimental method (most popular). You start with a sufficiently large distance. Every morning jump closer in front of the approaching car. One day the incoming car will crash into yours. Probably the distance in the previous day was absolutely minimal L min . Buy a new car, add some safety margin to L min and use this distance.
3. Safe experiment based on the theory. It is difficult to calculate the acceleration time (see method 1). However the acceleration time when you are trying to escape from the approaching car must be the same when you are chasing a car. If you turn immediately after a passing car (Fig.3) then the largest distance L can be used as the safe distance (again with some margin). You saved time and money and solved the problem (and did not disturb the traffic).
Fig.3. The initial distance 0
Fig.4. largest distance L
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©Nikolai V. Shokhirev, 2002-2005