Barth's belt slide rule
Date: dated 1921
Inventory Number: 1990-5-0006
Classification: Slide Rule
Dimensions:1.6 × 28.1 × 11.2 cm (5/8 × 11 1/16 × 4 7/16 in.)
DescriptionRectangular wooden rule with six slides, faced with off-white paper. The first, third, and sixth slides are fixed; the second, fourth, and fifth slides move to left and right.
Printed on the bottom edge of the top, fixed slide is a scale for "HORSE-POWER" and "REVOLUTIONS OF PULLEY PER MINUTE," carrying values from 1 to 500.
The top edge of the second, moveable slide is printed with a scale for "VELOCITY OF BELT PER MINUTE," with values ranging from 50' to 5000'. The bottom edge of the same (second) slide is printed with a scale for "DIAMETER OF PULLEY," carrying values from 3'' to 150''. To the right of this scale is an arrow pointing towards the third slide, labeled, "SET THIS ARROW TO PULL OF BELT AND READ HORSE-POWER OPPOSITE TO VELOCITY."
Printed along both the bottom and top edges of the third, fixed slide is a scale for "PULL AND INITIAL TENSION, IN POUNDS," with values ranging from 10 to 4000. Near the center of the top scale and pointing towards the second slide is an arrow labeled, "SET THIS ARROW TO DIAMETER AND READ VELOCITY OPPOSITE TO REVOLUTIONS."
Along the left side of the top edge of the fourth, moveable slide are six scales for "VELOCITY OF BELT." There is one pair each of vertically-stacked scales for, from left to right, a "HEAVY COUNTER-SHAFT BELT," a "LIGHT COUNTER-SHAFT BELT," and a "MACHINE BELT." The three top scales carry values (in thousands of feet) from 1 to 4. Below are scales with values (in hundreds of feet) descending from 11 to 0, 12 to 0, and 13 to 0, respectively. Immediately to the right of each pair of scales is the word "MINIMUM," printed perpindicular to the slide, as well as an arrow pointing towards the third slide and labeled, "MAX'M."
Along the right side of the top edge of the same (fourth) slide are six more scales for "VELOCITY OF BELT." Again there is one pair each of vertically-stacked scales for, from left to right, a "HEAVY COUNTER-SHAFT BELT," a "LIGHT COUNTER-SHAFT BELT," and a "MACHINE BELT." The three top scales carry values (in thousands of feet) descending from 3.5 to 1, 4 to 1, and 4.5 to 1 respectively. Below are scales with values (in hundreds of feet) ranging from 0 to 11, 0 to 12, and 0 to 13, respectively.
Along the left side of the bottom edge of the fourth slide are three arrows for "INITIAL TENSION OF BELT," pointing towards the fifth slide and labeled, from left to right, for a "HEAVY COUNTER-SHAFT BELT," a "LIGHT COUNTER-SHAFT BELT," and a "MACHINE BELT." Along the right side of the bottom edge of the same (fourth) slide are three arrows for "PULL OF BELT," again labeled for a "HEAVY COUNTER-SHAFT BELT," a "LIGHT COUNTER-SHAFT BELT," and a "MACHINE BELT."
To the far left of the fifth, moveable slide is a diagram showing a two-pulley belt system. The diameters of the larger and smaller pulleys ("D" and "d," respectively), as well as the distance between the pulleys ("C") are labeled. Immediately to the right of the diagram, along the bottom edge of the fifth slide, is a scale for "THICKNESS OF BELT," with values descending from 0.7'' to 0.1''. The values (in inches) from 11/16 to 9/16 are labeled for a "TRIPLE"; those from 7/16 to 5/16 are labeled for a "DOUBLE"; and those from 1/4 to 1/8 are labeled for a "SINGLE BELT."
Towards the center of the same (fifth) slide is an arrow labeled, "INITIAL TENS'N" and pointing towards the fourth slide. To the right of the arrow is printed a scale for:
"ARC OF CONTACT = (360°)[(square root)({[2-(D-d)]/C}/{[8+(D-d]/C})] FOR / OPEN BELT; (360°)(1-[(square root)({[2-(D+d)]/C}/{[8-(D+d]/C})]) FOR / CROSSED BELT"
It carries values from 120° to 240°.
Printed along the top edge of the bottom, fixed slide is a scale for "WIDTH OF BELT," carrying values from 1'' to 50''.
Signedface, right side of fifth and sixth slides: RULES FOR TRANSMISSION OF POWER / BY LEATHER BELTS AND IRON / PULLEYS ON MACHINE TOOLS ETC. Carl G. Barth
Inscribedface, left side of bottom slide: BARTH'S BELT SLIDE RULE. / IMPROVED AUGUST, 1921.
FunctionFor determining the velocity, initial tension, pull, and/or horsepower of a machine tool's belt system.
To determine the belt's velocity, the user first moves the second slide to left or right until the arrow on the top edge of the third slide points to the appropriate value on the diameter scale (second slide, bottom edge). He then locates the appropriate value on the revolutions scale (top slide). The coincident value on the scale on the top edge of the second slide indicates the belt's velocity (in feet per minute).
To determine the initial tension on the belt, the user first moves the fifth slide to left or right such that the appropriate value on the thickness scale (fifth slide, bottom edge) coincides with the appropriate value on the width scale (bottom slide). Holding the fifth slide in place, he then moves the fourth slide to left or right until the arrow labeled for the belt type in question (fourth slide, left half, bottom edge) is aligned with the initial tension arrow (fifth slide). He then locates the velocity value on the appropriate scale on the left half of the fourth slide. The coincident value on the pull/initial tension scale (third slide) gives the minimum initial tension. The arrow immediately to the right of the relevant velocity scale (fourth slide) points to the maximum initial tension
To determine the belt's pull, the user first moves the fifth slide to left or right such that the appropriate value on the thickness scale (fifth slide, bottom edge) coincides with the appropriate value on the width scale (bottom slide). Holding the fifth slide in place, he then moves the fourth slide to left or right until the arrow labeled for the belt type in question (fourth slide, right half, bottom edge) points to the appropriate value on the arc scale (fifth slide, top edge; arc may be calculated for either open or crossed belts using the equations shown). Finally, holding the fourth and fifth slides in place, the user locates the velocity value on the appropriate scale on the right half of the fourth slide. The coincident value on the pull/initial tension scale (third slide) indicates the belt's pull.
To determine the belt system's horsepower, the user moves the second slide to the right or left until the arrow on the right side of its bottom edge points to the appropriate pull value on the third slide's scale. Holding the second slide in place, he then locates the appropriate value on the velocity scale (second slide, top edge). The coincident value on the top slide's scale indicates the belt's horsepower.
Historical AttributesThis is part of a set of slide rules for machine shops designed by Carl G. Barth under Frederick Winslow Taylor's system of scientific management. Given the characteristics of a particular machine and a depth of cut, for example, a shop manager could quickly calculate the most efficient speed and feed settings using one of Barth's speed and feed slide rules. Other objects in the collection include slide rules for helical springs, belts, and gears, as well as jigs for making slide rules.
Primary SourcesCarl G. Barth, "Slide Rules for the Machine Shop as a Part of the Taylor System of Management," Transactions of the American Society of Mechanical Engineers 25 (1904): 49-62.
Frederick W. Taylor, "On the Art of Cutting Metals," Transactions of the American Society of Mechanical Engineers 28 (1908): 31-432.
ProvenanceThe papers and slide rules of Carl G. Barth and his son, J. Christian Barth, were transferred to the Baker Library of the Harvard Business School by J. Christian Barth in 1961.
The slide rules were transferred from Harvard Business School to the Collection of Historical Instruments in 1980.