majority">Horn, C. M.

The defendant is charged with the offense of operating a motor vehicle on a public highway in the borough of Queens, city of New York, at a rate of speed in excess of thirty-five miles per hour in violation of section 14 of article 3 of the Traffic Regulations of the City of New York, promulgated purstiant to section 435 of the New York City Charter, which regulation establishes the speed limits for automobiles operated within the city of New York.

This complaint was ordered by the court as a result of evidence presented before the magistrate at a criminal homicide hearing.

On December 1, 1939, at about six-thirty a. m., the defendant, while operating a Ford coach on Roosevelt avenue near Junction avenue in the county of Queens (following an accident), applied the brakes of his automobile, which locked and caused continuous tire skidmarks from all four wheels for a distance of over sixty-four feet and one inch in length upon a dry asphalt pavement.

About twenty minutes after the accident occurred, members of the homicide squad of the police department, in the course of their duties, arrived upon the scene, and after the skidmarks were identified by the defendant as having been caused by the tires of his automobile, measured their length. Only those skidmarks which were firm and continuous were taken into consideration. The testimony shows that the brakes were applied sooner, but since the first skidmarks were intermittent and not firm and continuous, measurements were only taken from the start of the firm, *237continuous skidmarks. Measuring from that point to the rear of the vehicle and then deducting its length, a measurement of sixty-four feet, one inch was determined. The four wheel brakes were then duly examined and being found to be in good working condition the same automobile was driven by one of the officers over the same stretch of roadway and when the speedometer recorded about thirty miles per hour the brakes were suddenly and firmly applied, causing similar skidmarks of forty-three feet three inches in length.

The only evidence in dispute is with respect to the length of the skidmarks made by defendant’s car. A lay witness, one Roper, who passed by following the accident, approximated them to be between thirty-five and forty feet long. In view of the fact that the police officers, who are specially trained for such investigations, made actual measurements, it is obvious that their figure is the correct one.

When questioned at the scene of the accident the defendant stated to a police officer that he had been driving his car at a speed of about thirty to thhty-five miles per hour at the time he applied his brakes. Outside of this admission by the defendant, who did not testify upon the trial, and the testimony of Mr. Roper, no evidence wras offered other than the testimony of the two members of the homicide squad who, after being qualified as experts, estimated the speed of the automobile on the basis of a mathematical formula.

While evidence of the speed of an automobile determined by the application of this formula has been used as evidence in both civil and criminal cases, none has come to the court’s attention where it was used as a basis for prosecuting a defendant for speeding. Usually the evidence relied upon in such cases is the testimony of police officers who, after following a defendant in a motor cycle or in an automobile, have “ clocked ” on the speedometer of their vehicle the speed at which the defendant is charged with having operated his automobile. This was so because no other means was devised for measuring speed.

The science of police work has made rapid strides within the last decade. Among other things, the homicide squad of the New York police department, in its desire to determine the cause of many accidents and in an endeavor to minimize them, caused an intensive study to be made of the relationship of skidmarks to that of the speed of an automobile in order to arrive at a formula whereby, based on certain known factors, the speed of an automobile, at the time of the commencement of the skid, might be determined. Lieutenant Andrews and Detective Grant in collaboration with Dr. F. C. Stanley, professor of physics and chemistry *238and technical research director for one of the large brake companies, and Mr. Tilden, professor of mechanical engineering, and also associated with one of the large brake' companies, studied the problem for about two years. As a result of their study, which included a series of scientific tests and compilation of statistics, they determined that by the application of the formula s ■ 30 f the speed of an automobile can be determined.

The formula is used by the New York police department, other agencies and brake companies. In interpreting this formula:

s equals distance of skid

v equals velocity (speed) of vehicle

30 equals gravitational constant in miles per hour (transformation of feet per second to miles per hour)

f equals coefficient of friction

A skidmark is caused by the burning of rubber from the tire as a result of the friction between the surface of the tire and the surface of the pavement (with brakes locked). This friction varies according to the holding power of the road surface. From thousands of tests made by the use of a drawbar and a dynometer, the coefficient of friction of pavements of streets throughout New York city has been determined. The coefficient of friction of asphalt pavement was determined to be .78. Others vary below and above, up to .95, which is the coefficient of brushed concrete.

The formula applied by the People has a valid basis in the science of physics and mathematics and is more clearly explained as follows: It is a fundamental truth that if a man travels 20 miles in four hours, his average velocity (speed) would be 5 miles per hour; in terms of a formula this would be

, ., distance average velocity =-or time

distance = average velocity X time or s = vaXt (1)

Acceleration is defined as change in speed per unit of time. When the speed is increasing, the acceleration is positive, and when the speed is decreasing, the acceleration is negative (or deceleration). To illustrate, the acceleration of a falling body is 32.2 feet per second; i. e., a body will fall at a rate of speed of 32.2 feet per second at the end of the first second, at a rate of speed of 64.4 feet at the end of the second second, etc. From this it will be observed that if the acceleration is constant the speed acquired will be directly proportional to the time. Take our example of *239the falling body, the speed (velocity) at any particular point in time will be the product of the number of seconds multiplied by 32.2 (the force of gravity — g);

v — 1st second = 1x32.2 or 32.2 ft. /sec.

v — 2nd second = 2x32.2 or 64.4 ft. /sec.

v — 3rd second = 3x32.2 or 96.6 ft. /sec.

etc.

Writing this in terms of a formula, we have

final velocity =. acceleration X time or

Any elementary physics book will tell us that the average velocity of a body moving with uniform acceleration equals one-half the sum of its initial and final velocity. Applying this to a falling body whose acceleration is accepted as fundamental, we would have a body starting from rest or a speed of zero to a velocity of 32.2 feet per second at the end of the first second. The distance covered, 16.1 feet in the first second, is elementary. The average speed or velocity would, therefore, be 16.1 feet per second. Written mathematically this would be

average velocity = A (initial velocity, plus,

final velocity) or

substituting

average velocity = A (0 plus 32.2)

average velocity = 16.1 or

when the initial velocity is zero. But substituting the value of Vi as found in formula (2), we have average velocity equals one-half acceleration times the time,

But formula (1) shows that distance traversed equals average speed (velocity) multiplied by time. Therefore, substituting the values in formula (4) for its equivalent in formula (1) we have

Reading this formula we may say that where the acceleration is constant, the distance traversed from rest varies as the square of the time.

*240

therefore, if a body starts from rest and acceleration is constant, the velocity varies as the square root of the distance traversed.

Physics has established that every body in motion possesses kinetic energy; that is, it will do a certain amount of work against a resisting force before it stops moving. The fundamental equation for the work done by any force acting through a distance is

Work = /Xs (7)

Whenever a force is acting on a body, the body has an acceleration in the direction in which the force acts and the acceleration is proportional to the force, that is

One way to get a force to act on a body is to let the body fall. In this illustration the force acting is known, for it is the weight (w) of the body. The acceleration is also known for it is gravity (</) which is 32.2 feet per second, per second. So that the weight of the body and its acceleration when falling can always be used as two of the numbers in the proportion just mentioned (8), that is,

substituting formula (9) in formula (7) we have

*241But the term as has been determined in formula (6) to be equal

transposing

of friction that is necessary to move a given weight over a given surface, or The coefficient of friction is determined by the pull or force

coefficient of friction = force of friction total normal pressure (weight) or

force of friction (/) = coefficient of friction X weight

/ = coef. of / X to

(13)

substituting this valuation of / in formula (12) we have

with weight canceling weight this resolves itself into

This formula represents velocity in feet per second. In order to change it to miles per hour, we make use of simple arithmetic, and

(Black & Davis, “ Practical Physics,” published by Macmillan Co. 1924.)

Applying the formula and using the known facts, we have

*242The witnesses Andrews and Grant were cross-examined at length both by counsel for defendant and the court as to various factors which might show that the formula was erroneous. They also testified that after having arrived at the formula they have experimented with it for a period of two and a half years and have found it substantially accurate. From all the evidence the court is satisfied beyond a reasonable doubt that the defendant was driving an automobile in excess of twenty-five miles per hour.

The defendant further argues, assuming the formula and computations to be correct, there still has been no violation proved, for the People have failed to show:

(1) That the speed limit at the particular point was twenty-five miles per hour.

(2) That the defendant was proceeding at a speed in excess of twenty-five miles per hour for at least one-quarter of a mile.

Section 14 of article 3 of chapter 14 of the Traffic Regulations of the City of New York provides:

“1. A driver of any vehicle shall not drive at a rate of speed faster than twenty-five miles per hour, except where signs authorized by proper authority are posted indicating a greater or lesser speed.

“ 2. No driver shall drive at a rate of speed faster than ten miles per hour when turning corner.”

There being no evidence before the court indicating that signs, authorized by proper authority, were posted indicating a greater or lesser speed, the general prohibition of a speed faster than twenty-five miles per hour must apply.

With respect to the second point raised, the defendant refers to the Vehicle and Trafile Law of the State of New York, paragraph b of subdivision 1 of section 56, which providesA rate of speed, by a motor vehicle other than a motor truck, in excess of forty miles an hour for a distance of one quarter of a mile, shall be presumptive evidence of driving at a rate of speed which is not careful and prudent.”

This contention of the defendant is erroneous, for the two statutes are entirely dissimilar. The regulation under which the defendant is being prosecuted is one which contains a specific prohibition against the operation of an automobile in excess of twenty-five miles per hour. The Vehicle and Traffic Law section of which the defendant has quoted a part also provides under paragraph a of subdivision 1 as follows: “ Every person operating a motor vehicle upon a public highway shall drive such vehicle in a careful and prudent manner and at a rate of speed so as not to endanger the property of another or the life or limb of any person.”

*243It is to be noted that the State statute does not prohibit driving at a speed in excess of a fixed rate of speed, but merely seeks to prohibit driving at a speed which is dangerous to the property or person of another. In that connection paragraph b merely creates the presumption that driving at a rate of speed in excess of forty miles per hour for a distance of one-quarter of a mile is a violation of the section. Its effect is merely to shift the burden of proof upon the defendant to show that, though exceeding forty miles per hour for a distance of a quarter of a mile, he was not under the circumstances driving in a careless or imprudent manner. In other words, speed alone is not the proper test of careless driving under the statute. (People v. Carrie, 122 Misc. 753; People v. Mellen, 104 id. 355.)

Furthermore, section 54 of the Vehicle and Traffic Law provides, “ and provided further that nothing in this chapter contained shall impair the validity or effect of any ordinances regulating the speed of motor vehicles * * * heretofore or hereafter made, adopted or prescribed pursuant, to law in any city of the first class.”

Hence, it is clearly apparent that the Legislature reserved to cities of the first class the power to regulate the speed of motor vehicles operated upon its streets.

Since section 435 of the New York City Charter gives the police department the power and duty to regulate, direct, control and restrict the movement of vehicular traffic, for the facilitation of traffic and the convenience of the public as well as the proper protection of human life and health, and the commissioner the power to make rules and regulations to accomplish that purpose, and since the provisions of section 14 of article 3 of chapter 14 of the Traffic Regulations of the City of New York are specific, evidence of speed in excess of twenty-five miles per hour, even though for a distance of less than one-quarter of a mile, would prove a violation of the regulation.

Under the circumstances, the defendant is found guilty, but due to the co-operation of the defendant and his counsel in the preparation and submission of this cause which is in the nature of a test case, sentence is suspended.

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