Download Report - Academy of Motion Picture Arts and Sciences

Download Report - Academy of Motion Picture Arts and Sciences Download Report - Academy of Motion Picture Arts and Sciences

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Since there is a steady diminution in the efficiency o{ the Tungsten lamp, it follows that there is some point in its life at which the use of any lamp should te ended, regardless of its actual life. In order to determine the truth of this theory and to find the length of the most economical time of use, two *"iitod. of computation are used; one by graphics; the other, by ordinary analytical algebraic calculation. The graphical I shall roughly sketch and then the anal]'tiial equation for the time of use, which is most ..otto*icul. The lamp is assumed to absorb 3,000 watts and deliver 66,000 lum-ens,. new' Figure ( 1) shows the curves' Curve No' 1 represents cost of lamp, per hour, and the ordinate for any value of time on the X axis, is equal to the original cost of the lamp, in cents, divided by the time for each value of X. For instance, if the lamp cost is 1,500 cents ($15) and the time o{ use 300 hours, the cost, per'hour, is 5 cents. For a use o{ 500 hours, tfie cost per hour of use is 3 cents' In this way the ordinates for curve No' 1 are computed and the curve plotted. Curves 2 and 3 are, respectively' the costs of current {or the lamp. Curve 2 is lor current at 1'45 cents per K. W. hour, and curve 3 is {or the rate of 2 cents per K. W. hour. Obviously, these are straight lines at the elevations 4.35 and and 6 respectfvely, the lamp being assumed as a 3 K' W' lamp, so that the cost' per lamp hour for-,current at 1.4j cents is 4.35 cents per hour, while at 2'00 cents per K. W. hour the cost is 6 cents per hour' The siraight line L--L, extending diagonally across the sheet, represents the lumens delivered by the lamp after any time of use as indicated by the ubscissae. The diminution in the lumens is assumed to be 40 per cent for 1000 hours of use. The curves C, and C" represents the total cost of operation of the lamp, per hour, at the current rates of 4.35 cents and 6 cents per lamp hour, respectively' These curves are plotted from ordinates obtained by adding to the ordinates of curve No. 1, the values 4,35, or 6 as the case may be. Curve C1 represents the total cost per hour for a lamp receiving current at 4.35 cents per hour, while curve C, shows the cost per hour for operating a lamp receiving current at 6 cents per hour' the cost of the lamp, per lamp hour, being included, as before indicated. The final curves, 4 and 5 show, respectively, the cost per lumen in cents per hour and the ordinates are Iound by dividing the total cost, in cents per hour, by the number of lumens given by the lamp at any plriod in its time of use. By plotting these final values it is seen that the curves, 4 and 5 droop downward for a certain time, then turn back upwards, showing a definite minimum value, which is marked on the figure' Of course, the results obtained graphically can be computed analytically. If K be the cost of the lamP in cents. If E be the cost of electricity per K' W. hour. If A be the energy consumption in K. W. ts0l If L be the lumens delivered by the lamp when new. If Q be the factor of reduction in lumens with use, or reduction of efrciency per hour of usage. If X be the time of use, or number of hours of use at which the point of maximum economy is attained: Then QX will be the reduction in the output of iumens at the end oi the period o{ use, X. The lamp cost, distributed over the total time of K use, X, is - gsn15 per hour. X The current cost is EA cents per hour. Lumens output after X hours will be L-LQX which is equal to L(l-QX). K EA+X Then the total cost per lumen i5 --- gsn65. L( 1_QX) EAX+K L( l-QX) .....-..( 1 ) Differentiating, and equating to zero to determine the time period, X, which gives the minimum cost per lumen. OV - - LEAQX' + 2KLQX - KL :O...-.-.(2) dx (2KLQ) KL Whence, X'?+X- which re- (LEAQ) LEAQ duces to, dy2KK dx EA EAQ *t/ffir'K Whence,X - I V - -Fl -- - -(4) EAQ \EA7 EA Obviously, only the positive value before the radical can be used, because there is no negative value of elapsed time. By substituting thc proper numerical values the economic length of time for use of the lamp can be computed. Note that the value of X is independent of the actual quantity of lumens which the lamp delivers, the term "L" having cancelled out in the derivation of the formula. Example : K, or lamp cost, $15, or 1,500 cents. E, the current cost, 2 cents per K. W. hour. A, the energy consumption, 3 K. W. Q, the reduction in efficiency with time of use taken at 40 per cent for 1,000 hours, and therefore 0.4 of the total illumination within that time. This is equal to a diminution of 0.0004 per cent of the lumens new per hour,

Then for these numerical values, Y-V r/ffiz r 2x3x0.0004 2x3 2x3 r,soo Which is equal to { 625p901 62,500 - 250. Which is equal to 829 - 250, or X : 579 hours. By substituting in the equation (4) all of the above lrulrr.., except ihat for current costr making "E''' !!" cost per K. W. hour, 1.45 cents' and solving for X, the time of use, which results in maximum economy' is found to be 646 hours. These two values check fairlY found graphically and shown in ure 1. DISCUSSION ON DR. LYNDON'S PAPER well with those the curves, Fig- t s1 l Mn. Fanmnala: The lamp manufacturers use a method sbmewhat similar to that described by Dr. Lyndon to determine the most economic and best lamp life. By proper choice of the lamp efficiency (filament temperature) the average life of lamps may be controlled within wide limits. Based on lamp renewal costs alone, if the cost of electrical .n.igy is low and lamp costs very high, then it *o*ld b" desirable to design the lamps for a fairly long life and conversely if the energy cost is high and lu-p cost low, it would be more economical to operate the lamps at a short life. In the case of Iamps used for general lighting service it has been found that for the average energy rates prevailing throughout the country an average life o{ about 500-600 hours gives the maximum light at lowest cost, In the case of lamps for studio lighting service we have the additional important element of color of the light. It would be desirable from the standpoint of color rendition on the film to operate the lamps at a very short life; i. e., 50 or 100 hours; this, however, would make the lamp cost excessive. In our study of the problem, it has been found that a life of from 200 to 400 hours gives the best balance between energy cost, lamp cost, and the photographic rendition of colors. Several studios are making the mistake of operating their lamps at a long life, hoping to reduce their lamp costs. While such a procedure may reduce the lamp expense, it greatly reduces the quantity of photographic light from the lamp with the result that more equipment must be used to secure sufficient light, and as equipments cost more than lamps the net operating expense may be higher. QuBsrrox: Has there been reached a comparison between the two lights, the Arc and the Incandescent as to the amount of light that we require for a given amount of space? In large sets the Arc lights seem to have a greater carrying power naturally and without occupying a considerable amount of space. Do the Incandescents have a tendency to drop ofi in carrying power? As the light proceeds from the lamp it is absorbed by the atmosphere. Close to the lamp there would be a great deal of energy. We have never come around to that point. In other words, would Mazda illumination be possible for general illumination without having to resort to Arc lights for certain things at some future time ? Mn. Bar,r-: Who can answer? Mr. Jones. Mn. JoNns: I did not get the import of the question. QursuoN: In the relative quality of the lights in making up the comparison between the Arc light and the Incandescent, it seems that the rays of the carbon lamp will travel to a greater extent than the Incandescent. The Incandescent has a greater falling off power for a given area. A large set lighted with Incandescents would require more lamps than an Arc lighted set. Mn. JoNrs: The question is rather complicated, and the answer, I think, depends upon the definition of the term "falling off." There are reliable data relative to the penetrating power of difierent wave lengths. In the case of the transmission of light through the earth's atmosphere, which contains a certain amount of diffusing or scattering material, such as water, vapor and dust, red light will travel with less loss of intensity than blue, which is scattered to a greater extent. Light from the Incandescent lamp is red, compared with that of the Arc, and hence under the conditions mentioned above should travel with less loss of intensity than Arc light. In the studio, however, this atmospheric scattering must be very small indeed, and hence will have a negligible efiect. If the Arcs actually have greater "carrying power" in the studio it is probably due to difierences in the angular distribution of the radiation from the light source, the light source being defined as the actual source of radiation plus its reflection fixture or housing. It may be also that this opinion that the Arc carries better than Tungsten light is based upon tests in which care has not been exercised to be certain that the two sources have identical candle-powers. Mn. FanwHau: Mr. Jones' statements relative to the greater power of red light in penetrating {og and dust are correct. I should like to supplement Mr. Jones' remarks with reference to the carrying power of light from various sources. Ever since I have made a study of the lighting problems in the studios, the statement has been made that the light from Incandescent sources falls ofi more rapidly with increasing distance than does the light from the Arc lamp. The illumination received on any surface follows what is called the inverse .qrr"r. I"*, and is independent of the nature of the source. A simple statement of the inverse square law is: The illumination intensity on a surface varies inversely as the square of the distance between that sur{ace and the light source. I should like, at this time.

Then for these numerical values,<br />

Y-V<br />

r/ffiz<br />

r<br />

2x3x0.0004 2x3 2x3<br />

r,soo<br />

Which is equal to { 625p901 62,500 - 250.<br />

Which is equal to 829 - 250, or<br />

X : 579 hours.<br />

By substituting in the equation (4) all <strong>of</strong> the above<br />

lrulrr.., except ihat for current costr making "E''' !!"<br />

cost per K. W. hour, 1.45 cents' <strong>and</strong> solving for X,<br />

the time <strong>of</strong> use, which results in maximum economy'<br />

is found to be 646 hours.<br />

These two values check fairlY<br />

found graphically <strong>and</strong> shown in<br />

ure 1.<br />

DISCUSSION ON<br />

DR. LYNDON'S PAPER<br />

well with those<br />

the curves, Fig-<br />

t s1 l<br />

Mn. Fanmnala: The lamp manufacturers use<br />

a method sbmewhat similar to that described by Dr.<br />

Lyndon to determine the most economic <strong>and</strong> best<br />

lamp life. By proper choice <strong>of</strong> the lamp efficiency<br />

(filament temperature) the average life <strong>of</strong> lamps<br />

may be controlled within wide limits. Based on<br />

lamp renewal costs alone, if the cost <strong>of</strong> electrical<br />

.n.igy is low <strong>and</strong> lamp costs very high, then it<br />

*o*ld b" desirable to design the lamps for a fairly<br />

long life <strong>and</strong> conversely if the energy cost is high<br />

<strong>and</strong> lu-p cost low, it would be more economical to<br />

operate the lamps at a short life. In the case <strong>of</strong><br />

Iamps used for general lighting service it has been<br />

found that for the average energy rates prevailing<br />

throughout the country an average life o{ about<br />

500-600 hours gives the maximum light at lowest<br />

cost,<br />

In the case <strong>of</strong> lamps for studio lighting service we<br />

have the additional important element <strong>of</strong> color <strong>of</strong><br />

the light. It would be desirable from the st<strong>and</strong>point<br />

<strong>of</strong> color rendition on the film to operate the<br />

lamps at a very short life; i. e., 50 or 100 hours;<br />

this, however, would make the lamp cost excessive.<br />

In our study <strong>of</strong> the problem, it has been found that a<br />

life <strong>of</strong> from 200 to 400 hours gives the best balance<br />

between energy cost, lamp cost, <strong>and</strong> the photographic<br />

rendition <strong>of</strong> colors.<br />

Several studios are making the mistake <strong>of</strong> operating<br />

their lamps at a long life, hoping to reduce<br />

their lamp costs. While such a procedure may reduce<br />

the lamp expense, it greatly reduces the quantity<br />

<strong>of</strong> photographic light from the lamp with the<br />

result that more equipment must be used to secure<br />

sufficient light, <strong>and</strong> as equipments cost more than<br />

lamps the net operating expense may be higher.<br />

QuBsrrox: Has there been reached a comparison<br />

between the two lights, the Arc <strong>and</strong> the Inc<strong>and</strong>escent<br />

as to the amount <strong>of</strong> light that we require<br />

for a given amount <strong>of</strong> space? In large sets the Arc<br />

lights seem to have a greater carrying power naturally<br />

<strong>and</strong> without occupying a considerable amount<br />

<strong>of</strong> space. Do the Inc<strong>and</strong>escents have a tendency to<br />

drop <strong>of</strong>i in carrying power? As the light proceeds<br />

from the lamp it is absorbed by the atmosphere.<br />

Close to the lamp there would be a great deal <strong>of</strong><br />

energy. We have never come around to that point.<br />

In other words, would Mazda illumination be possible<br />

for general illumination without having to resort<br />

to Arc lights for certain things at some future<br />

time ?<br />

Mn. Bar,r-: Who can answer? Mr. Jones.<br />

Mn. JoNns: I did not get the import <strong>of</strong> the<br />

question.<br />

QursuoN: In the relative quality <strong>of</strong> the lights<br />

in making up the comparison between the Arc light<br />

<strong>and</strong> the Inc<strong>and</strong>escent, it seems that the rays <strong>of</strong> the<br />

carbon lamp will travel to a greater extent than the<br />

Inc<strong>and</strong>escent. The Inc<strong>and</strong>escent has a greater falling<br />

<strong>of</strong>f power for a given area. A large set lighted<br />

with Inc<strong>and</strong>escents would require more lamps than<br />

an Arc lighted set.<br />

Mn. JoNrs: The question is rather complicated,<br />

<strong>and</strong> the answer, I think, depends upon the definition<br />

<strong>of</strong> the term "falling <strong>of</strong>f." There are reliable data<br />

relative to the penetrating power <strong>of</strong> difierent wave<br />

lengths. In the case <strong>of</strong> the transmission <strong>of</strong> light<br />

through the earth's atmosphere, which contains a<br />

certain amount <strong>of</strong> diffusing or scattering material,<br />

such as water, vapor <strong>and</strong> dust, red light will travel<br />

with less loss <strong>of</strong> intensity than blue, which is scattered<br />

to a greater extent. Light from the Inc<strong>and</strong>escent<br />

lamp is red, compared with that <strong>of</strong> the Arc,<br />

<strong>and</strong> hence under the conditions mentioned above<br />

should travel with less loss <strong>of</strong> intensity than Arc<br />

light. In the studio, however, this atmospheric scattering<br />

must be very small indeed, <strong>and</strong> hence will<br />

have a negligible efiect. If the Arcs actually have<br />

greater "carrying power" in the studio it is probably<br />

due to difierences in the angular distribution <strong>of</strong><br />

the radiation from the light source, the light source<br />

being defined as the actual source <strong>of</strong> radiation plus<br />

its reflection fixture or housing. It may be also that<br />

this opinion that the Arc carries better than Tungsten<br />

light is based upon tests in which care has not<br />

been exercised to be certain that the two sources<br />

have identical c<strong>and</strong>le-powers.<br />

Mn. FanwHau: Mr. Jones' statements relative<br />

to the greater power <strong>of</strong> red light in penetrating {og<br />

<strong>and</strong> dust are correct. I should like to supplement<br />

Mr. Jones' remarks with reference to the carrying<br />

power <strong>of</strong> light from various sources. Ever since I<br />

have made a study <strong>of</strong> the lighting problems in the<br />

studios, the statement has been made that the light<br />

from Inc<strong>and</strong>escent sources falls <strong>of</strong>i more rapidly<br />

with increasing distance than does the light from the<br />

Arc lamp. The illumination received on any surface<br />

follows what is called the inverse .qrr"r. I"*,<br />

<strong>and</strong> is independent <strong>of</strong> the nature <strong>of</strong> the source. A<br />

simple statement <strong>of</strong> the inverse square law is: The<br />

illumination intensity on a surface varies inversely<br />

as the square <strong>of</strong> the distance between that sur{ace<br />

<strong>and</strong> the light source. I should like, at this time.

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