PRG4090E-C_COVER.
INTRODUCTION The custom-designed Sheet Metal/HVAC Pro Calc calculator was specifically created for sheet metal pro’s to ease the task of performing mathematics on the job. It includes the most popular built-in formulas for sheet metal computations, so you’ll save time, increase accuracy and eliminate errors.
TABLE OF CONTENTS KEY DEFINITIONS ............................................................................6 BASIC OPERATION KEYS.............................................................6 CONVERT Ç KEY—UNIT CONVERSIONS and SECOND FUNCTIONS................................................................6 MEMORY and STORAGE FUNCTIONS ........................................7 RECALL ® KEY ..........................................................................8 FEET-INCH-FRACTION and METRIC KEYS ....
Dividing Dimensions ..................................................................29 Percentage Calculations ............................................................30 MEMORY OPERATION ................................................................31 EXAMPLES — USING THE SHEET METAL/HVAC PRO ..............33 BASIC EXAMPLES .......................................................................34 Adding Linear Measurements ....................................................
Dividing Offset into Multiple Degreed Elbows for Manageable Sections .............................................................51 Change OGEE Offset ................................................................53 LAW OF COSINES EXAMPLES...................................................55 Field Measuring for Ductwork Using the Law of Cosines Introduction .............................................................................
Rise ............................................................................................88 Rise and Diagonal......................................................................88 Sheathing Cut ............................................................................89 Regular Hip/Valley and Jack Rafters .........................................89 Jack Rafters — Using Other Than 16 Inch On-Center Spacing ...................................................................................
KEY DEFINITIONS BASIC OPERATION KEYS o O +–x ÷= Ç+ On/Clear — Turns power on. Pressing once clears the display. Pressing twice clears all temporary values. Turns all power off, clearing all non-permanent registers. Arithmetic operation keys. Percent (%) — Four-function percent. See page 30 for examples. 0 – 9 and • Keys used for entering digits. B Backspace Key — Used to delete entries one keystroke at a time (unlike the o function, which deletes the entire entry).
Ç√ Ç/ Ç÷ Ç – Cube Root Function — Used to find the Cube Root of a non-dimensional or volume value (e.g., 1 0 0 0 Ç √ = 10). x10 y — Allows entry of an exponent. For example, 8 Ç / 1 4 is 8 times 10 to the 14th power (8x1014). 1/x — Finds the reciprocal of a number (e.g., 8 Ç ÷ = 0.125). Change (+ / –) Sign — Changes the sign of the displayed value to negative or positive. Pi — Constant = 3.141593 π Çπ Ç• ArcK — Constant = 0.017453.
Ç1 Storage Register (M1) — Stores the displayed value in non-cumulative, permanent Memory (e.g., 1 0 Ç 1, ® 1 = 10). Good for storing a single value, for future reference. Note: Non-cumulative means it only accepts one value (does not add or subtract) and a second entered value will replace the first. Permanent means the value is stored even after the calculator is shut off. To delete a stored value, enter a new value or perform a Clear All (Ç x). Ç2 Ç3 Storage Register (M2) — Same function as Ç 1.
i Enters or converts to Inches. Also used with the / key for entering fractional inch values (e.g., 9 i 1 / 2). Note: Repeated presses after Ç toggle between Fractional and Decimal Inches (e.g., 9 i 1 / 2 Ç i = 9.5 INCH; press i again to return to Inch-Fractions). / m Çm Fraction Bar — Used to enter Fractions. Fractions may be entered as proper (1/2, 1/8, 1/16) or improper (3/2, 9/8). If the denominator (bottom) is not entered, the calculator's fractional resolution setting is automatically used (e.g.
Your calculator has standard trigonometric keys, in addition to Right Triangle keys (e.g., R, r, d and p), for advanced Right Triangle mathematics. The Sine, Cosine, and Tangent of an angle are defined in relation to the sides of a Right Triangle. Using the Ç key with the trigonometric function gives you the Arcsine, Arccosine and Arctangent – all of which are used to find the Angle for the Sine, Cosine, or Tangent value entered.
Using the Pythagorean Theorem, the top row of keys on your Sheet Metal/HVAC Pro Calc provides instant solutions in dimensional format to Right Triangle problems for sheet metal problems and roof framing. The Right Triangle is calculated simply by entering two of four variables: 1) 2) 3) 4) R r d x (Run) y (Rise) r (Diagonal, or Hypotenuse); or θ (Theta/Pitch). Run — Enters or calculates “x,” or the Run or horizontal leg (base) of a Right Triangle.
LAW OF COSINES / NON-90 DEGREE TRIANGLE KEYS Ç9 Law of Cosines — These keys are used for non-90 degree triangle mathematics and are incorporated with Right Triangle mathematics (using “Measured” non-90 degree and “Calculated” Right Triangles), particularly, for finding the dimensional relationship of distance and alignment between two or more objects. The overall purpose of these calculations is to develop the duct and/or fittings required to fill a space.
Right Triangle Functions: R r d p Length of Unknown Side — Calculates Side “x” of unknown Right Triangle. Length of Unknown Side — Enters Side “y” of unknown Right Triangle. Hypotenuse — Enters “c” of Measured Triangle as “r” of unknown Right Triangle, for final determination of “x” and “y.” Theta — Finds unknown angle for determination of “x” and “y.
FAN LAW KEYS Your calculator also has built-in formulas and keys that calculate Fan Laws 1, 2 and 3, for air flow calculations. Each of these formulas requires the entry of three variables in order to solve the fourth. ÇR Çr Çd Fan Law 1 — Calculates the missing variable (e.g., “a-new” or “b-new” for CFM new or RPM new) for Fan Law 1, given the three known variables into the applicable Storage Registers (see below). See page 75 for examples. Fan Law 2 — Calculates the missing variable (e.g.
VELOCITY PRESSURE / FPM KEYS Ç0 VP ß © FPM — Converts entry to Velocity (Feet per Minute - FPM), Velocity Pressure, Metric Velocity (MPS) and Metric Velocity Pressure (kPA). Press 1 2 3 4 Result Calculates Velocity (FPM) – assumes entry is Velocity Pressure Calculates Velocity Pressure – assumes entry is Velocity (FPM) Calculates Metric Velocity (MPS) – assumes entry is kPA Calculates Metric Velocity Pressure (kPA) – assumes entry is MPS See page 46 for examples.
(Cont’d) If a Circle Diameter is entered into the C key and Arc Degree (or Arc Length) entered into the Arc function (Ç C), further presses of C will display and calculate the following: Press 1 2 3 4 5 6 7 8 9 Result Arc Length or Degree of Arc Chord Length Segment Area Pie Slice Area Segment Rise Stored On-Center Spacing Length of Arched Wall 1 Length of Arched Wall 2 Length of Arched Wall 3 (if applicable), etc.
HIP/VALLEY and JACK RAFTER KEYS Your calculator uses the y (rise), x (run), r (diagonal), θ (pitch), and o.c. spacing values to calculate Regular (45°) and Irregular (non-45°) Hip/Valley and Jack rafter lengths (excluding wood thickness, etc.). When calculating Regular and Irregular Jack rafter lengths, you will see the letters “JK” (Common Pitch side) or “IJ” (Irregular Pitch side) and the corresponding Jack number to the left of your calculator display.
(Cont’d) • Subsequent presses of the H key will also display Plumb, Level, and Cheek cut angle values in degrees. ÇH Irregular Pitch — Enters the Irregular or Secondary Pitch value used to calculate lengths of the Irregular Hip/Valley and Jack rafters. You may enter the Irregular Pitch as: • a Dimension: 9 i Ç H • an Angle: 3 0 Ç H • a Percentage: 7 5 Ç + Ç H Note: An entered Irregular Pitch can be recalled by pressing ® Ç H.
Çj STAIR KEY Irregular Side Jacks — Operates same as j, but displays the rafter values from the irregular pitched side first. Your calculator easily calculates stair layout solutions. Given values for r (Rise) and/or R (Run), your calculator will calculate Riser, Tread, Stringer and Angle of Incline values simply by pressing the s key.
Çs Ç== == Store Desired Riser Height — Stores a value other than the default desired stair Riser height of 7-1/2 Inches (e.g., 8 i Ç s stores an eight-inch desired stair Riser height). To recall the stored setting, press ® s. Store Desired Tread Width — Stores a value other than the default desired stair Tread width of ten inches. See page 107 Preference Settings to view how to use the + and – key to increase or decrease stored Tread width.
GETTING STARTED You may want to practice getting a feel for your calculator keys by reading through the key definitions and learning how to enter basic Feet-Inch-Fractions and Metric, how to store values in Memory, etc., before proceeding to the examples. You may also want to glance at various formulas listed in the Appendix, so you understand what mathematical calculations your calculator is programmed to perform, or common formulas you can refer to on the job.
USING PARENTHESES Your calculator has Parentheses keys ( and ) for performing mathematical operations. (In the Order of Operations method, expressions inside of parentheses are performed first.) The calculator offers four levels of parenthesis: 1) First parenthesis level opened – press ( for one RightSided Parenthesis. 2) Second level opened – press ( a second time for two Right-Sided Parentheses ( (. 3) Third level opened – press ( a third time for three RightSided Parentheses ( ( (.
SETTING FRACTIONAL RESOLUTION Your calculator is set to display fractional answers in 16ths, and all examples in this User Guide are, therefore, based on 1/16ths. However, you may select the fractional resolution to be displayed in other formats (e.g., 1/64ths, 1/32nds, etc.). Follow the two options for selecting fractional resolution below. Setting Fraction Resolution to Other Than 16ths — Using the Preference Setting Mode KEYSTROKE 1.
Setting Fixed/Constant Fractional Resolution You can also program your calculator so that the displayed fraction will always show in the fractional resolution you have set (following the above instructions). That is, instead of solving for the closest fraction, it will always display the chosen fractional resolution. For example, if you have chosen 1/64ths, 1/2 will be displayed as 32/64. If you do not use this feature, Standard Fractional Resolution will be displayed.
ENTERING DIMENSIONS Entering Linear Dimensions When entering Feet-Inch-Fraction values, enter dimensions from largest to smallest — e.g., Feet before Inches, Inches before Fractions. Enter Fractions by entering the numerator (top), pressing / (Fraction bar key) and then the denominator (bottom). Note: If a denominator is not entered, the fractional setting value is used. Examples (press o after each one): DIMENSION 5 Feet 1-1/2 Inch 17.
Examples of Square and Cubic Entry: FEET f f — Square Feet (e.g., 5 f f will display 5. SQ FEET). f f f — Cubic Feet (e.g., 5 f f f will display 5. CU FEET). INCHES i i — Square Inches (e.g., 5 i i will display 5. SQ INCH). i i i — Cubic Inches (e.g., 5 i i i will display 5. CU INCH). METERS m m — Square Meters (e.g., 5 m m will display 5. SQ M). m m m — Cubic Meters (e.g., 5 m m m will display 5. CU M). MILLIMETERS Ç m m — Square Millimeters (e.g., 5 Ç m m will display 5.
CONVERSIONS (LINEAR, AREA, VOLUME) Linear Conversions Convert 14 Feet to other dimensions: KEYSTROKE DISPLAY 0. 14 FEET 168 INCH 4.267 M 4267.2 MM oo 14f Çi m* Ç m (mm) *Note: When performing multiple conversions, you only have to press the Ç key once (except when accessing secondary functions (Millimeters), e.g., Ç m). Converting Feet-Inch-Fractions to Decimal Feet Convert 15 Feet 9-1/2 Inches to Decimal Feet. Then convert back to Feet-Inch-Fractions. KEYSTROKE oo 15f9i1/2 Çf f DISPLAY 0.
Converting Decimal Inches to Fractional Inches Convert 9.0625 Inches to Fractional Inches. Then convert to Decimal Feet. KEYSTROKE DISPLAY 0. 9.0625 INCH 9-1/16 INCH 0.755208 FEET oo 9•0625i Çi ff Square Conversions Convert 14 Square Feet to other Square dimensions: KEYSTROKE oo 14ffÇi m Ç m (mm) DISPLAY 0. 2016. SQ INCH 1.300643 SQ M 1300642.56* SQ MM *For larger digit displays, the numerator section is utilized for decimal displays.
PERFORMING BASIC MATH WITH DIMENSIONS Adding Dimensions KEYSTROKE DISPLAY Add 11 Inches to 2 Feet 1 Inch: 11i+2f1i= 3 FEET 0 INCH Add 5 Feet 7-1/2 Inches to 18 Feet 8 Inches: 5 f 7 i 1 / 2 + 1 8 f 8 i = 24 FEET 3-1/2 INCH Subtracting Dimensions KEYSTROKE Subtract 3 Feet from 11 Feet 7-1/2 Inches: 11f7i1/2–3f= Subtract 32 Inches from 81 Inches: 81i–32i= DISPLAY 8 FEET 7-1/2 INCH 49 INCH Multiplying Dimensions KEYSTROKE Multiply 5 Feet 3 Inches by 11 Feet 6-1/2 Inches: 5 f 3 i x 1 1 f 6 i 1 /
Percentage Calculations Percent (Ç +) is used to find a given percent of a number or to perform add-on, discount or division percentage calculations. You may also perform percentage calculations with dimensional units (Feet, Inch, etc.), in any format (Linear, Square or Cubic).
MEMORY OPERATION Your calculator has two types of Memory operations: 1) A Standard, Cumulative, Semi-permanent Memory µ; and 2) Three Storage Registers [M1], [M2] and [M3], used to permanently store single, non-cumulative values. Memory commands are listed below.
i. Basic Cumulative Memory (M+) Example 1: Store 100 into M+, add 200, then subtract 50. Clear the Memory: KEYSTROKE DISPLAY M+ 100. M M+ 200. M M– 50. M M+ 250. 100µ 200µ 50ǵ ®® Note: To Clear Memory (M+): - press ® ®; or - turn off the calculator. Example 2: Store 100 into M+, then replace this value with 200 using Memory Swap: KEYSTROKE DISPLAY M+ 100. M 100. M SWAP 100. M M+ STORED 200. M M+ 200. M+ 100µ ®µ 200Ç® ®µ ®® ii.
EXAMPLES — USING THE SHEET METAL/HVAC PRO The Sheet Metal/HVAC Pro Calc calculator has keys and functions labeled in common sheet metal/HVAC or construction terms. Just follow the examples and adapt the keystrokes to your specific application. Your calculator will save you time; you don’t need to remember common formulas, as they are built into timesaving keys.
BASIC EXAMPLES Adding Linear Measurements Find the total length of the following measurements: 5 Feet 4-1/2 Inches, 8 Inches and 3.5 Meters. KEYSTROKE DISPLAY 1. Add the measurements: oo 5f4i1/2+ 8i+ 3•5m 2. Find the total: = 5 6 17 FEET FEET FEET 0. 4-1/2 INCH 0-1/2 INCH 3.
Adding and Subtracting Fractions of an Inch Add 1/2 Inch, 3/8 Inch and 11/16 Inch. Then subtract 5/8 Inch. KEYSTROKE oo 1/2+3/8+11/16= –5/8= Converting Fractions to Decimals DISPLAY 1-9/16 0-15/16 0. INCH INCH Convert 7/32 Inch and 1/3 Inch to Decimals, respectively (and round answers): KEYSTROKE oo 7/32Çi 1/3Çi Converting Decimals to Fractions DISPLAY 0. 0.21875 INCH (Answer = 0.219”) 0.333333 INCH (Answer = 0.33”) Convert 5.875 Inches and 8.
Circumference of a Circle Find the Circumference of a Circle if its Radius is 8 Feet 4 Inches: KEYSTROKE oo 8f4iÇp C C Circumference and Area of a Circle DISPLAY RAD 8 FEET 4 DIA 16 FEET 8 CIRC 52 FEET 4-5/16 0. INCH INCH INCH Find the Area and Circumference of a Circle with a Diameter of 11 Inches: KEYSTROKE oo 11iC C C Square Area (x 2) DISPLAY 0. DIA 11 INCH CIRC 34-9/16 INCH AREA 95.
Area of a Triangle Find the Area of a Triangle if its base is 45 Inches and Altitude/ Height is 30 Inches. KEYSTROKE oo 45i÷2= x30i= Volume of a Rectangular Box DISPLAY 0. 22-1/2 INCH 675. SQ INCH Find the Volume of a rectangular box with Length of 15 Inches, Width of 6 Inches and Height 9-1/2 Inches. KEYSTROKE oo 15ix6ix9i1/2= DISPLAY 855. 0.
Volume of a Cylinder Calculate the Volume of a Cylinder with a Diameter of 2 Feet 4 Inches and a Height of 4 Feet 6 Inches: *Note: For a Cylinder, use the Column ) function. KEYSTROKE DISPLAY 1. First, enter Diameter to find Circle Area: oo 0. 2f4iC DIA 2 FEET 4 INCH CC AREA 4.276057 SQ FEET 2. Enter Height and find Volume of Column (or Cylinder): 4f6ir Y 4 FEET 6 INCH Ç) COL 19.
Cubed Function What is the Cubed value of 10? What is 503? KEYSTROKE DISPLAY 0. 1000. 125000. oo 10ÇX 50ÇX Cubed Root Function Example 1: What is the Cubed Root of 100? Then, find KEYSTROKE : DISPLAY 0. 4.641589 17.1995 oo 100Ç√ 5088Ç√ Example 2: What are the three dimensions of a Cube with a Volume of 2028 Cubic Inches? KEYSTROKE oo 2028Ç√ Alternate method of entry using Unit Keys: KEYSTROKE oo 2028iii Ç√ Çii Scientific Notation DISPLAY 0. 12.65773 (Inches) DISPLAY 0.
TRIGONOMETRIC FUNCTIONS Trigonometric functions are available on the Sheet Metal/HVAC Pro Calc calculator. The drawing and formulas below list basic trigonometric formulas, for your reference: Given side A and angle a, find: Side C A÷aç = (i.e.
Finding Sine, Cosine, Tangent Find Sine 12°, Cosine 33° and Tangent 75°: KEYSTROKE oo 12S 33ç 75t Finding “Angle A” (ArcSin, ArcCos, ArcTan) DISPLAY 0. 0.207912 0.838671 3.732051 Find Angle A if Sine A = 0.57544, Cosine A = 0.06753 and Tangent A = 0.87421 and round to the nearest whole angle: KEYSTROKE oo •57544ÇS •06753Çç •87421Çt Using Trigonometry to Find Unknown Side DISPLAY 0. 35.13045° (35°) 86.12787° (86°) 41.
Using Trigonometry to Find Unknown Angle or Side Example 1 — Cos A: Solve for the unknown angle A if the two known sides are: Side b = 15 mm Side c = 35 mm a) Longhand Method: In this case, use the trigonometry formula: Cos = Adjacent/Hypotenuse or cos A = b/c KEYSTROKE oo 1 5* ÷ 3 5 = Ç ç Ç• *Note: you do not have to label mm. DISPLAY 0. 64.62307° (64.6°) DMS 64.37.23 b) Alternative Method (Use Pythagorean Theorem Keys): Insert values into x, y, or r keys to solve for Theta.
Trig Examples (Cont’d) Example 2 — Sin A: Solve angle A of the offset below, if the two known sides are: Side a = 8 Inches Side c = 25 Inches In this case, use the trigonometry formula: Sin = Opposite/Hypotenuse or Sin A = a/c a) Longhand/Use Sine Formula: KEYSTROKE oo 8÷25=ÇS b) Use Pythagorean Theorem Keys: KEYSTROKE oo 8r 25d p DISPLAY 0. 18.66292° (18.7°) DISPLAY 0. Y 8. R 25. /_ Ø 18.66292° (18.
Trig Examples (Cont’d) Example 3 — Tan A: Find the length of the transition for a 20° angle: Side a = 18 Inches Side b = unknown a) Longhand Method: Use Tan = Opposite/Adjacent KEYSTROKE DISPLAY 1. First solve for Tan 20° to find ratio, then enter in Memory: oo 0. 20tµ M+ 0.36397 M 2. Solve for Side b by dividing Side a by stored ratio: 18÷®µ= 3. Clear Memory and clear display: ®®o b) Use Pythagorean Theorem Keys: KEYSTROKE oo 18r 20p R 44 — SHEET METAL/HVAC PRO CALC 49.45459 M (49.5 inches) 0.
Converting Pitch to Angle/Tangent Find the angle and corresponding Tangent for a roof with an 8/12 Pitch: KEYSTROKE DISPLAY 1. Enter Pitch: oo 8ip PTCH 8 2. Convert Pitch to degrees: p 0. INCH /_ Ø 33.69007° 3. Find Tangent or slope: pp 0.666667 D:M:S EXAMPLE Converting Degrees:Minutes:Seconds Convert 23°42’39” to Decimal Degrees: KEYSTROKE oo 23•42•39 Ç • (degrees) DISPLAY Convert 44.29° to degrees:minutes:seconds format: KEYSTROKE oo 4 4 • 2 9 Ç • (d:m:s) 0. DMS 23.42.39 23.
VELOCITY PRESSURE / VELOCITY EXAMPLES The Velocity Pressure/Velocity function uses an entered value to calculate these four values: Number entered is assumed to Velocity Pressure 2. Velocity (Pressure) Number entered is assumed to Velocity (FPM) 3. Metric Velocity (MPS) Number entered is assumed to Metric Velocity Pressure (kPA) 4. Metric Velocity Pressure Number entered is assumed to (kPA) Metric Velocity (MPS) 1.
Converting FPM to Velocity Pressure Calculate the Velocity Pressure (Imperial and Metric) if the FPM is 500: KEYSTROKE 1. Enter 500 FPM to calculate Velocity: oo 500Ç0 2. Calculate Velocity Pressure (VP): 0* 3. Calculate Metric Velocity (MPS): 0 4. Calculate Metric Velocity Pressure (KPA): 0 5. Re-display entered value: 0 DISPLAY 0. FPM 89554.52 VP 0.015586 MPS 29.06888 KPA 147928.99 500. *The VP ß ©FPM function begins with the last displayed value.
OFFSET EXAMPLES Offset, Basic Example If an offset is 5 Feet, the actual Length 10 Feet, and the Height of the “end A” equal to 7 Feet, calculate the Centerline Radius, Wrapper Length, Heel Radius, Throat Radius, and Theta. KEYSTROKE DISPLAY 1. Enter actual Length as “x”: oo 10fR 2. Enter offset Length as “y”: 5fr 3. Enter Height of “end A” as “a”: 7fÇ4 A 0. X 10 FEET 0 INCH Y 5 FEET 0 INCH 7 FEET 0 INCH STORED 4.
OGEE Offset in Feet-Inch-Fractions If an offset is 12-5/8 Inches, the actual Length 45 Inches, and the Height of the “end A” is 38 Inches, calculate the Centerline Radius, Wrapper Length, Heel Radius, Throat Radius, and Theta. KEYSTROKE DISPLAY 1. Enter actual Length as “x”: oo 45iR 2. Enter offset Length as “y”: 12i5/8r 3. Enter Height of “end A” as “a”: 38iÇ4 A 0. X 45 INCH Y 12-5/8 INCH 38 INCH STORED 4.
OGEE Offset, in Millimeters If an offset is 573 Millimeters (mm), the actual Length 2045 mm, and the Height of the “end A” 1727 mm, calculate the Centerline Radius, Wrapper Length, Heel Radius, Throat Radius, and Theta. *Note: To save keystrokes, you do not have to label entries in mm. KEYSTROKE DISPLAY 1. Enter actual Length as “x”: oo 2045ÇmR 2. Enter offset Length as “y”: 573Çmr 3. Enter Height of “end A” as “a”: 1727ÇmÇ4 A 0. X 2045. MM Y 573. MM 1727. MM STORED 4.
Dividing Offset into Multiple Degreed Elbows for Manageable Sections Solve the offset using the given variables: Actual Length “x”: 80-1/2 Inches Offset Length “y”: 22-9/16 Inches A: 68 inches Then, divide Theta into four degreed elbows; double Theta for two equal elbows. KEYSTROKE DISPLAY 1. Enter actual Length as “x”: oo 80i1/2R 2. Enter offset Length as “y”: 22i9/16r 3. Enter Height of “way end A” as “a”: 68iÇ4 A 0.
(Cont’d) KEYSTROKE DISPLAY 4. Calculate Centerline Radius, Wrapper Length, Heel Radius, Throat Radius and Theta: Ç( RAD 77-7/16 INCH ( WL 84-5/8 INCH ( HEEL 111-7/16 INCH ( THRT 43-7/16 INCH ( THET 15.6571° 5. Convert Theta to degrees:minutes:seconds:* Ç• 6. Multiply by two to double offset:** x2= DMS 15.39.25 DMS 31.18.51 *The angle of Theta can be used to divide the offset into degreed elbows for more manageable sections.
Change OGEE Offset Solve the Change OGEE Offset below, with Wrapper Size transitions from one end to another. A) Solve Using: a. Actual Length “x”: 52-5/8 Inches b. Offset “y”: 15-3/16 Inches c. End “a”: 34 Inches KEYSTROKE DISPLAY 1. Enter actual Length as “x”: oo 52i5/8R 2. Enter offset Length as “y”: 15i3/16r 3. Enter Height of “way end A” as “a”: 34iÇ4 A 0. X 52-5/8 INCH Y 15-3/16 INCH 34 INCH STORED 4.
B) Solve Using: a. Actual Length “x”: 52-5/8 Inches b. Offset “y”: 25-3/16 Inches c. End “a”: 34 Inches KEYSTROKE DISPLAY 1. Enter actual Length as “x”: oo 52i5/8R 2. Enter offset Length as “y”: 25i3/16r 3. Enter Height of “end A” as “a”: 34iÇ4 A 0. X 52-5/8 INCH Y 25-3/16 INCH 34 INCH STORED 4. Calculate Centerline Radius, Wrapper Length, Heel Radius, Throat Radius and Theta: Ç( RAD 33-13/16 INCH ( WL 60-5/16 INCH ( HEEL 50-13/16 INCH ( THRT 16-13/16 INCH ( THET 25.
LAW OF COSINES EXAMPLES Field Measuring for Ductwork Using the Law of Cosines — Introduction Dimensions taken when measuring objects in the field are taken from the plan or horizontal plane and the elevation or vertical plane of the objects. The purpose is to find the dimensional relationship of distance and alignment between two or more objects. In the Sheet Metal Industry, these specific dimensions are identified as Length, Offset, and Angle.
Non-90 Degree Triangle Measurement Using Law of Cosines and Heron’s Theorem The Law of Cosines keys calculate the unknown angles after inputting the three known sides of a non-90 degree triangle. Triangle area is also found given the built-in formula for Heron’s Theorem. The relationship of any side to the included angle is identified as the angles opposite the side having the same letter designation (see diagram on next page).
(Cont’d) KEYSTROKE DISPLAY 1. Enter side a, b and c: oo 38f5iÇ4 A STORED 38 FEET 5 23f4i9/16Ç5 B STORED 23 FEET 4-9/16 26f1i13/16Ç6 C STORED 26 FEET 1-13/16 2. Calculate Angle A, B and C: Ç9 9 9 3. Calculate Triangle area: 9 0. INCH INCH INCH /_ A 101.5734° /_ B 36.59978° /_ C 41.8268° AREA 299.
Using Law of Cosines and Pythagorean Theorem to Calculate Offset, Length, and Angle In field measuring, Offset, Length and Angle are the essential dimensions to the design and fabrication of the components required to fill in between objects. In some cases, no structural objects are within reach or parallel to the objects to be measured, so other methods of measuring are required. In this method, a Triangle is formed to establish the relationship between the objects.
(Cont’d) KEYSTROKE DISPLAY 1. Enter side a, b and c: oo 3 5 f 8 i 3 / 4 Ç 4 A STORED 35 FEET 8-3/4 21f8i15/16Ç5 B STORED 21 FEET 8-15/16 2 4 f 3 i 7 / 8 Ç 6 C STORED 24 FEET 3-7/8 0. INCH INCH INCH 2. Calculate and input Theta by subtracting Angle “A” (found by the Law of Cosines) from known angle of 180°: 180–Ç9 /_ A 101.5687° = 78.43128 (Theta θ) p /_ Ø 78.43128° 3. Recall stored “c” and input as “r” the Hypotenuse: ®6=d R 24 4. Calculate “x”: R 5.
Inline Duct, Single Offset (Computing Offset, Length, and Angle) When working with the process of direct measure between two ducts #1 and #2, as diagramed below, one leg of “The Measured Triangle” “I” should use the larger horizontal dimension of the two ducts. Therefore, in this scenario, the 42 Inches dimension of duct #2 is used since it is the larger of the two ducts.
(Cont’d) KEYSTROKE 1. Enter side a, b, and c: oo 8f2i3/8Ç4 42iÇ5 6f10iÇ6 DISPLAY A STORED C 8 B STORED 0. 2-3/8 INCH STORED 42 INCH 6 FEET 10 INCH FEET 2. Calculate and input Theta by subtracting Degree “A” (found by the Law of Cosines) from known angle of 180°: 180–Ç9 /_ A 99.94554° = 80.05446 (Theta θ) p /_ Ø 80.05446° 3. Recall stored “c” and input as “r”: ®6=d 4. Calculate “x”: R 5.
Inline Duct, Double Offset (Computing Offset, Length and Angle) This example (see diagrams below) depicts two ducts offsetting both in the horizontal and vertical planes. Basic procedures are the same as those followed in the previous example, except a correction to the calculated length will be required at triangle “V”. A) Input “Measured Triangle I” to find Triangle IV: KEYSTROKE 1. Enter side a, b, and c: oo 2509ÇmÇ4 2096ÇmÇ5 1067ÇmÇ6 DISPLAY A B C STORED STORED STORED 2509. 2096. 1067. 0.
B) Input “Measured Triangle II” to find Triangle III: KEYSTROKE 1. Enter side a, b, and c: oo 2088ÇmÇ4 2096ÇmÇ5 356ÇmÇ6 DISPLAY A STORED 2088. B STORED 2096. C STORED 356. 0. MM MM MM 2. Calculate and input Theta by subtracting Degree “A” (found by the Law of Cosines) from known angle of 90° (in this case, the Triangles form a Right Triangle): 90–Ç9 /_ A 83.83727° = 6.162732 (Theta θ) p /_ Ø 6.162732° 3. Recall stored “b” and input as “r”: ®5=d 4. Calculate “x”: R 5. Calculate “y”: r R 2096.
C) Input Triangle V to Find Actual Length Between the Objects: KEYSTROKE DISPLAY 1. Enter “y” from Triangle IV and enter as “r” (the Hypotenuse): oo 0. 2065Çmd R 2065. MM 2. Enter “y” from Triangle III and enter as “y”: 225Çmr Y 225. 3. Calculate “x” for the Actual Length between the objects: R X 2052.
Objects at Right Angles When you are working with objects at Right Angles, set up the “Measured Triangles” and subsequent calculations in the same manner as the previous inline objects. Due to the vertical misalignment of the two ducts, the added step of finding the actual length will be required. With the exception of the duct dimensions the measured lengths of Triangle III are slant lengths. Therefore, if the calculations are processed using these dimensions the results would also be slant lengths.
1) Find the elevation offset “Ye” and the actual length “Xe” in D1: KEYSTROKE DISPLAY 1. Enter sides a, b, and c: oo 0. 7 f 9 i 7 / 1 6 Ç 4 A STORED 7 FEET 9-7/16 INCH 2f2iÇ5 B STORED 2 FEET 2 INCH 7 f 1 1 i 1 / 8 Ç 6 C STORED 7 FEET 11-1/8 INCH 2. Calculate and input Theta by subtracting Degree “A” (found by the Law of Cosines) from Right Angle of 90°: 90–Ç9 /_ A 78.40512° = 11.59488 (Theta θ) p /_ Ø 11.59488° 3. Recall stored slant length “c” and input as “r”: ®6=d R 7 4.
2) Find actual length “Xe” in D2: KEYSTROKE 1. Enter slant length as “r”: oo 11f8i13/16d DISPLAY R 11 FEET 0. 8-13/16 INCH 2. Enter calculated elevation offset from D1 as “y”: 1f7i1/8r Y 1 FEET 7-1/8 INCH X 11 FEET 7-1/2 INCH 3.
3) Find the horizontal length ”Xp” between the objects and the horizontal offset “Yp” between the objects: KEYSTROKE DISPLAY 1. Enter sides a, b and c: oo 0. 1 1 f 7 i 1 / 2 Ç 4 A STORED 11 FEET 7-1/2 INCH 5f2iÇ5 B STORED 5 FEET 2 INCH 7 f 9 i 3 / 1 6 Ç 6 C STORED 7 FEET 9-3/16 INCH 2. Calculate and input Theta by subtracting Degree “A” (found by the Law of Cosines) from 180°: 180–Ç9 /_ A 126.8649° = 53.13512 (Theta θ) p /_ Ø 53.13512° 3. Recall stored “c” and input as “r”: ®6=d R 7 FEET 9-3/16 4.
Calculating Angles Between Objects (“Angle Between”) The Triangle, having a total of 180°, is the basic logic used to solve for the angle between two objects. To accomplish this task, two measurable Triangles are established between the objects for the purpose of finding the angles C, A, and A2, as indicated in the example below. Subtracting the sum of Angles C, A, and A2 from 180° gives us the “Angle Between” the two objects.
Calculating Angles Between Objects Example LEGEND 1 Existing Roof Curb to remain. 2 New 20’ x 20’ duct down through Roof Curb to system below. 3 New Roof Top Furnace with integral curb. 4 Field measure duct required from the existing roof to new Roof Top Furnace. 5 Existing Roof Drain to remain.
1) Find actual length “y” between objects in D1: KEYSTROKE DISPLAY 1. Enter side a, b, and c: oo 8f11i11/16Ç4 A STORED 8 FEET 11-11/16 1f7iÇ5 B STORED 1 FEET 7 8f8i1/8Ç6 C STORED 8 FEET 8-1/8 0. INCH INCH INCH 2. Calculate and input Theta by subtracting Degree “A” (found by the Law of Cosines) from known angle of 180°: 180–Ç9 /_ A 95.70871° = 84.29129 (Theta θ) p /_ Ø 84.29129° 3. Recall stored “c” and input as “r”: ®6=d 4. Calculate “x”: R 5.
2) Find actual length “y” between objects in D2: KEYSTROKE DISPLAY 10i3/8R 9f8i9/16d r 3) Find actual length “y” between objects in D3: KEYSTROKE 10i3/8R 10f2i11/16d r 72 — SHEET METAL/HVAC PRO CALC X 10-3/8 INCH R 9 FEET 8-9/16 INCH Y 9 FEET 8-1/8 INCH DISPLAY X 10-3/8 INCH R 10 FEET 2-11/16 INCH Y 10 FEET 2-1/4 INCH
4) Input Triangle I and find Angles A and C: KEYSTROKE DISPLAY 1. Enter side a, b, and c: oo 2f2iÇ4 A STORED 2 FEET 2 STORED 10f2i1/4Ç5 B 10 FEET 2-1/4 9f8i1/8Ç6 C STORED 9 FEET 8-1/8 0. INCH INCH INCH 2. Use Law of Cosines to find Angle “A” and store in Memory 1: Ç 9 /_ A 12.17384° =Ç1 M-1 12.17384° 3. Use Law of Cosines to find Angle “C” and store in Memory 2: Ç999 /_ C 70.36573° =Ç2 M-2 70.
5) Input Triangle II and find Angle A1 and the “Angle Between”: KEYSTROKE DISPLAY 1. Enter side a2, b2, and recall c (“a2” was calculated as “y” in first section; “c” is already stored): o 0. 8f7i5/8Ç4 A STORED 8 FEET 7-5/8 INCH 2fÇ5 B STORED 2 FEET 0 INCH STORED ®6 C 9 FEET 8-1/8 INCH 2. Use Law of Cosines to find Angle “A2” and store in Memory 3: Ç9 /_ A 53.40618° =Ç3 M-3 53.40618° 3. Recall M1, M2, and M3 and find total: ®1+®2+®3= 4. Add total to M+ (regular Memory): µ 135.9458° M+ 135.
FAN LAW EXAMPLES Fan Law 1 The formula for Fan Law 1 (built into this calculator) is: where, CFM = Feet 3 per Minute RPM = Revolutions per Minute Fan laws use the temporary storage registers a, b, a-new, and b-new. Fan Law 1 calculates using the entry of the three known variables and Ç R to calculate the unknown fourth value. Example 1: A 1,250 CFM fan is running at 750 RPM, but it needs to supply 1,400 CFM. What is the RPM required? KEYSTROKE 1. Enter current CFM into “a” old: oo 1250Ç4 2.
Fan Law 2 The formula for Fan Law 2 (built into this calculator) is: S S where, SP = Static Pressure CFM = Feet 3 per Minute Fan laws use the temporary storage registers a, b, a-new, and b-new. Fan Law 2 calculates using the entry of the three known variables and Ç r to calculate the unknown fourth value. Example 1: A fan is producing 15,300 CFM at 3.2” SP. If the fan is adjusted to 14,000 CFM, what will the new SP be? KEYSTROKE 1. Enter current CFM into “a” old: oo 15300Ç4 2.
Fan Law 3 The formula for Fan Law 3 (built into this calculator) is: where, BHP = Brake Horsepower CFM = Feet 3 per Minute Fan laws use the temporary storage registers a, b, a-new, and b-new. Fan Law 3 calculates using the entry of the three known variables and Ç d to calculate the unknown fourth value. Example 1: A fan is running at 15,800 CFM using 6.3 BHP. If the CFM is increased to 20,000 CFM, what is the new BHP? KEYSTROKE 1. Enter current CFM into “a” old: oo 15800Ç4 2.
ARC / CIRCLE EXAMPLES Arc Length — Degree and Diameter Known Find the Arc length of an 85° portion of a Circle with a 5-Foot Diameter: KEYSTROKE oo 5fC 85ÇC C Arc Length — Degree and Radius Known DISPLAY 0. DIA 5 FEET 0 INCH ARC 85.00° ARC 3 FEET 8-1/2 INCH Find the Arc length of a Circle with a 24-Inch Radius and 77° of Arc (77° of 360° Circle): KEYSTROKE oo 2 4 i Ç p (Segment Radius) 77ÇC C Using ArcK to Calculate an Arc Length DISPLAY 0. RAD 24 INCH ARC 77.
Arc Calculations — Arc Length and Diameter Known Find the Arc Degree, Chord Length, Rise, Segment and Pie Slice Area, and Segment Rise, given a 5-Foot Diameter and an Arc length of 3 Feet 3 Inches: KEYSTROKE DISPLAY 1. Enter Circle Diameter (Note: enter Diameter into the C key): oo 0. 5fC DIA 5 FEET 0 INCH 2. Enter Arc Length: 3f3iÇC 3. Find Degree of Arc: C 4. Find Chord Length: C 5. Find Segment Area: C 6. Find Pie Slice Area: C 7. Find Segment Rise: C ARC 3 FEET 3 INCH ARC 74.
Arched/Circular Rake-Walls — Chord Length and Segment Rise Known You’re building a Circular or Arched Rake-Wall. Given a Chord Length of 15 Feet and a Rise of 5 Feet, find all Arc values and lengths of the Arched walls. The On-Center spacing is 16 Inches. KEYSTROKE 1. Enter Chord Length and Segment Rise: oo 15fR 5fr 2. Calculate Radius: Çp 3. Find Arc Angle: ÇC 4. Find Arc Length: C 5. Display entered Chord Length: C 6. Find Segment Area: C 7. Find Pie Slice Area: C 8.
(Cont’d) KEYSTROKE 10. Find Arched wall stud lengths: C C C C C DISPLAY AW1 4 FEET 10-11/16 AW2 4 FEET 6-5/8 AW3 3 FEET 11-3/8 AW4 3 FEET 0-1/16 AW5 1 FEET 6-1/4 Note: Successive presses of C will toggle to the beginning. INCH INCH INCH INCH INCH Arched Windows Find the Radius of an Arched window with a Chord Length of 2 Feet 7 Inches and a Rise of 10-1/2 Inches. Then, find the Arc Angle, Arc Length and Segment Area of the window. KEYSTROKE 1. Enter Chord Length: oo 2 f 7 i R (Run) 2.
CONCRETE/PAVING Squaring-up a Foundation A concrete foundation measures 23 Feet 8 Inches by 45 Feet 6 Inches. Find the diagonal measurement (Square-up) to ensure the form is perfectly square. KEYSTROKE 1. Enter sides as Rise/Run: oo 2 3 f 8 i r (Rise) 4 5 f 6 i R (Run) 2. Find the Square-up (Diagonal): d Volume of a Rectangle DISPLAY Y 23 X 45 R 51 FEET FEET FEET 8 6 3-7/16 0.
Volume of Columns Find the Volume of five (5) Columns, if each has a Diameter of 3 Feet 4-1/2 Inches and a Height of 11 Feet 6 Inches. Note: Use the Column/Cone function ( Ç ) ). KEYSTROKE 1. Find Circle Area: oo 3f4i1/2 CCC DISPLAY 0. 3 FEET 4-1/2 INCH AREA 8.946176 SQ FEET 2. Enter Height and find the total Volume for five Columns: 1 1 f 6 i r (Rise) Y 11 FEET 6 INCH Ç) COL 102.881 CU FEET x5= 514.
RIGHT TRIANGLE and ROOF FRAMING EXAMPLES Roof Framing Definitions y (Rise): The vertical distance measured from the wall’s top plate to the intersection of the pitch line and the center of the ridge. Span: The horizontal distance or full width between the outside edges of the wall’s top plates. x (Run): The horizontal distance between the outside edge of the wall’s top plate and the center of the ridge; in most cases this is equivalent to half of the span.
Rafters: Rafters are inclined roof support members. Rafters include the following types: • Common Rafter: The Common connects the plate to the ridge and is perpendicular to the ridge. • Hip Rafter: The Hip rafter extends from the corner of two wall plates to the ridge or King rafter at angle other than 90°. The Hip rafter is an external angle of two planes. • Valley Rafter: The Valley rafter extends from the corner of two wall plates to the ridge or King rafter at angle other than 90°.
Plumb: Vertical Cut. The angle of cut from the edge of the board that allows the rafter to mate on the vertical side of the ridge rafter. Level: Horizontal Cut. The angle of cut from the edge of the board that allows the rafter to seat flat on the wall plate. Cheek: Side Cut(s). The angle to cut from the SIDE of the Jack rafter to match up against the Hip or Valley rafter, usually made by tilting the blade from 90°. Jack rafters typically have one Cheek cut.
Common Rafter Length If a roof has a 7/12 Pitch and a Span of 14 Feet 4 Inches, what is the Point-to-Point length of the Common rafter (excluding the overhang or ridge adjustment)? What are the Plumb and Level cuts? KEYSTROKE DISPLAY 1. Find Diagonal or Point-to-Point length of the Common rafter: oo 0. 7ip PTCH 7 INCH 14f4i÷2= 7 FEET 2 INCH R X 7 FEET 2 INCH d R 8 FEET 3-9/16 INCH 2. Find Plumb and Level cuts: d d Common Rafter Length — Pitch Unknown PLMB 30.25644° LEVL 59.
Angle and Diagonal (Hypotenuse) Find the Diagonal (Hypotenuse) and Degree of Angle of a Right Triangle that is 9 Feet high and 12 Feet long. KEYSTROKE 1. Enter Rise and Run: oo 9fr 12fR DISPLAY Y 9 X 12 FEET FEET 0 0 0. INCH INCH 2. Solve for Diagonal/Hypotenuse, Pitch in Inches and Degree of Angle: d R 15 FEET 0 INCH p PTCH 9 INCH p /_ Ø 36.8699° Rise Find the Rise given a 7/12 Pitch and a Run of 11 Feet 6 Inches. KEYSTROKE oo 7ip 11f6iR r Rise and Diagonal DISPLAY 0.
Sheathing Cut You have framed an equal Pitch roof and need to apply the roof sheathing. Find the distance from the corner of the sheathing so that you can finish the Run at the Hip rafter and cut the material. The Pitch is 6 Inches and you are using 4-Foot by 8-Foot plywood, with the 8-Foot side along the plate. KEYSTROKE DISPLAY 1. Enter Pitch: oo 6ip PTCH 6 2. Enter width of plywood: 4fd 3. Find length of sheathing: R Regular Hip/Valley and Jack Rafters R 4 X 3 FEET 0.
(Cont’d) KEYSTROKE DISPLAY 2. Find Hip/Valley rafter length and cut angles: H H/V 12 FEET 10-1/2 INCH H PLMB 22.41512° H LEVL 67.58488° H CHK1 45.° 3. Find Jack rafter lengths and cut angles: j JKOC 16 INCH* j JK1 8 FEET 2-3/8 INCH j JK2 6 FEET 7-7/8 INCH j JK3 5 FEET 1-3/8 INCH j JK4 3 FEET 6-13/16 INCH j JK5 2 FEET 0-5/16 INCH j JK6 0 FEET 5-13/16 INCH j JK7 0 FEET 0 INCH j PLMB 30.25644° j LEVL 59.74356° j CHK1 45.
Jack Rafters — Using Other Than 16 Inch On-Center Spacing A roof has a 9/12 Pitch and a Run of 6 Feet 9 Inches. Find the Jack rafter lengths and cut angles at 18-Inch (versus 16-Inch) On-Center spacing. The On-Center spacing is used for both Regular and Irregular Jack calculations. KEYSTROKE 1. Enter Pitch, Run, and On-Center spacing: oo 9ip 6f9iR 18ijj 2. Find Jack rafter lengths and cut angles: j j j j j j j j 3. Reset On-Center spacing to 16 Inches: 16ij DISPLAY 0.
Irregular Hip/Valley and Jack Rafters — Descending, with On-Center Spacing Maintained You’re working with a 7/12 Pitch and half your overall Span is 4 Feet. The Irregular Pitch is 8/12, and 16-Inch On-Center spacing is maintained on both sides.
(Cont’d) KEYSTROKE DISPLAY 5. Find Irregular Jack Plumb, Level, and Cheek cut angles: j PLMB 33.69007° j LEVL 56.30993° j CHK1 41.18592° 6. Find Regular Jack lengths: j j j j JKOC STORED 16 JK1 2 FEET 10-3/8 JK2 1 FEET 1-1/4 JK3 0 FEET 0 INCH INCH INCH INCH 7. Find Regular Jack Plumb, Level, and Cheek cut angles: j PLMB 30.25644° j LEVL 59.74356° j CHK1 48.
STAIR LAYOUT EXAMPLES Stair Layout Definitions y (Rise): The “floor-to-floor” or “landing-to-landing” Rise is the actual vertical Rise required for building a stairway after the finish flooring has been installed. x (Run): The Run of a stairway is the amount of horizontal space required. The total Run of a stairway is equal to the width of each Tread multiplied by the number of Treads.
Number of Risers: The number of Risers includes both the first and the last Riser of the stairway. Riser Overage or Underage: The Riser Overage or Underage is the difference between the “floor-to-floor” Rise and the total height of all of the Risers. Many times the Riser height does not divide evenly into the floor-to-floor Rise and a small fraction of an Inch is left over. A positive remainder is an Overage, while a negative remainder is an Underage.
Stairs — Given Only Floor-to-Floor Rise You’re building a stairway with a total Rise of 9 Feet 11 Inches. Your desired Riser height is 7-1/2 Inches and desired Tread width is 10 Inches. The desired Headroom is 6 Feet 8 Inches and Floor Thickness 10 Inches*. Find all stair values, then calculate the Run. *Note: Headroom and Floor Thickness are required to calculate the height of the stairwell opening. KEYSTROKE 1. Enter known Rise: oo 9f11ir DISPLAY Y 9 FEET 11 2.
To Change Desired Riser Height: If you wish to use a desired Riser height of other than 7-1/2 Inches (the calculator’s default), simply enter a new value. For example, to enter eight Inches, enter 8 i Ç s. Press ® s to review your new entry. This value will be permanently stored until you change it.
Stairs — Given Only the Run You’re building a stairway with a total Run of 20 Feet. Your desired Riser height is 7-1/2 Inches and desired Tread width is ten Inches (default, or preset values). The desired headroom is 6 Feet 8 Inches and floor thickness 10 Inches (defaults). Find all stair values, then calculate the Rise. KEYSTROKE 1. Enter Run: oo 20fR DISPLAY X 20 FEET 0 0. INCH 2.
Stairs — Given Rise and Run You need to build a stairway with a floor-to-floor height of 10 Feet 1 Inch, a Run of 15 Feet 5 Inches, and a nominal desired Riser height of 7-1/2 Inches (default). Calculate all stair values. KEYSTROKE 1. Enter Rise and Run: oo 10f1ir 15f5iR 2. Find stair values: s s s s s s s s s s s s s s s DISPLAY Y 10 X 15 FEET FEET 1 5 0. INCH INCH R-HT 7-9/16 INCH* RSRS 16. R+/– 0 INCH T-WD 12-5/16 INCH TRDS 15.
Baluster Spacing You are going to install a handrail at the top of a balcony. Your total Span is 156 Inches and you would like the space between the balusters to be about 4 Inches. If each baluster is 1-1/2 Inches wide, what is the exact spacing between each baluster? KEYSTROKE 1. Estimate number of balusters in Span: oo 156i÷ 5 i 1 / 2 =* DISPLAY 0. 156 INCH 28.36364 (28 balusters) *desired spacing plus baluster width (4 Inches plus 1-1/2 Inches). 2.
APPENDIX A — TRIGONOMETRY FORMULAS The Sine of an angle is the ratio of the opposite side over the Hypotenuse: Sine Sin = Opposite Hypotenuse c A b a sin A = The Cosine of an angle is the ratio of the adjacent side over the Hypotenuse: Cosine Cos = Adjacent Hypotenuse c A b a cos A = The Tangent of an angle is the ratio of the opposite side over the adjacent side: Tangent Tan = Opposite Adjacent c A b a tan A = a c b c a b USER’S GUIDE — 101
APPENDIX B — AREA / VOLUME FORMULAS AREA FORMULAS 102 — SHEET METAL/HVAC PRO CALC
SURFACE AREA / VOLUME FORMULAS USER’S GUIDE — 103
APPENDIX C — OFFSET FORMULAS With Offset = “y” and Length = “x,” θ = ArcSin Offset Offset ( SlantLength )= ArcTan( Length )= ArcTan( xy ) CenterlineRadius = SlantLength2 SlantLength = 4Sin(θ) 4 * Offset WrapperLength (aka StretchOut) = CenterlineRadius * ArcK * 4θ HeelRadius = CenterlineRadius + (a ÷ 2) ThroatRadius = CenterlineRadius – (a ÷ 2) 104 — SHEET METAL/HVAC PRO CALC
APPENDIX D — LAW OF COSINES / HERON’S THEOREM FORMULAS Law of Cosines A c b B a Law of Sines a R Heron’s Theorem Tan b2 = c2 + a2 – 2cacosB c2 = a2 + b2 – 2abcosC C A b C a2 = b2 + c2 – 2bccosA ( A2 )= s –r a a c sin A B s= Tan = b sin B = c sin C = 2R 1 (a + b + c) 2 ( B2 )= s –r b Tan ( C2 )= s –r c USER’S GUIDE — 105
APPENDIX E — FAN LAW FORMULAS Fan Law 1 Formula Fan Law 2 Formula S S Fan Law 3 Formula where, CFM = Feet 3 per Minute RPM = Revolutions per Minute where, SP = Static Pressure CFM = Feet 3 per Minute where, BHP = Brake Horsepower CFM = Feet 3 per Minute APPENDIX F — DEFAULT SETTINGS After a Full Reset/Clear All, your calculator will return to the following settings: SETTING On-Center Spacing Fractional Resolution Area Display Volume Display Desired Riser Height Desired Tread Width Stairway Headroom F
APPENDIX G — PREFERENCE SETTINGS Your calculator has Preference Settings that allow you to customize or set desired dimensional formats and calculations. See the list of Settings below and instructions how to set them on the following page.
(Cont’d) PREFERENCE 3) Volume Display Format 4) Tread Width 5) Stairwell — Headroom Height 6) Floor Thickness 7) Jack Rafters Descending or Ascending OPTIONS — *Standard (if units entered are the same — e.g., Feet x Feet x Feet — the answer will remain in this format (Cubic Feet), but if units entered are different — e.g., Feet x Feet x Inches — volume answer will always be displayed in Cubic Feet) — Cubic Feet (volume answers always displayed in Cubic Feet, regardless of unit entry — e.g.
(Cont’d) PREFERENCE 8) Irregular Jack Rafters O-C or Mate 9) Exponent Off or On 10) Meter Linear Display 11) Degrees Displayed 12) Mathematical Operations 13) Fractional Mode OPTIONS — *OC-OC (On-Center spacing maintained on both Regular and Irregular sides) — JAC-JAC (Regular/Irregular Jack rafters “mate” at the Hip/Valley, i.e., OnCenter spacing not maintained on both sides) — *On (Exponential Mode is On; turns on Auto-Ranging; i.e.
How to Set Preferences The following sections detail Preference Setting options. Enter the Preference Mode by pressing Ç = (Prefs). Access each category by pressing the = key until you reach the desired setting. Within each category, press the + or – keys to toggle between individual selections. Press o to exit and set in your Preference. Note: + will advance, – will back up. Pressing the = key continuously in this mode will revolve the Preference Settings full circle.
Accessing Preference Settings To Set “Fractional Resolution”: KEYSTROKE Ç = (Prefs) (first press of =) + (plus sign) + + + + To Set “Area” Answer Format: KEYSTROKE = (second press of =) + (plus sign) + To Set “Volume” Answer Format: KEYSTROKE = (third press of =) + (plus sign) + DISPLAY FRAC 0-1/16 FRAC 0-1/32 FRAC 0-1/64 FRAC 0-1/2 FRAC 0-1/4 FRAC 0-1/8 = (fourth press of =) +* (plus sign increases height by 1/4 Inch) –* (minus sign decreases height by 1/4 Inch) INCH INCH INCH INCH INCH DISPLAY AR
(Cont’d) To Increase or Decrease Floor Thickness from Default of 10”: KEYSTROKE = (sixth press of =) +* (plus sign increases height by 1 Inch) –* (minus sign decreases height by 1 Inch) FLOR 10 FLOR 11 FLOR 10 *Keep pressing plus or minus to increase or decrease an Inch at a time.
(Cont’d) To Set Mathematical Operations Method: KEYSTROKE DISPLAY MATH OrdEr MATH CHAIn = (twelfth press of =) + (plus sign) To Set Fractional Mode: KEYSTROKE DISPLAY FRAC Std. FRAC COnSt FRAC Std. = (thirteenth press of =) + (plus sign) + (repeats options) Note: Press o at any time to exit the Preference Mode. To Reset your calculator to the default Preference Settings, turn off your calculator, hold down the multiplication x key, and turn on.
APPENDIX I — ACCURACY, AUTO SHUT-OFF, BATTERIES, ERRORS Accuracy/Errors Accuracy/Display Capacity — Your calculator has a twelve-digit display made up of eight digits (normal display) and four fractional digits. You may enter or calculate values up to 19,999,999.99. Each calculation is carried out internally to ten digits. Errors — When an incorrect entry is made, or the answer is beyond the range of the calculator, it will display the word “ERROR.
Auto Shut-Off Your calculator is designed to shut itself off after about 8-12 Minutes of non-use. Battery(ies) • Two LR44 batteries. Replacing the Battery(ies) Should your calculator display become very dim or erratic, replace the battery(ies). Note: Please use caution when disposing of your old battery, as it contains hazardous chemicals. Replacement batteries are available at most discount or electronics stores. You may also call Calculated Industries at 1-775-885-4975.
REPAIR AND RETURN WARRANTY, REPAIR AND RETURN INFORMATION Return Guidelines 1. Please read the Warranty in this User's Guide to determine if your Sheet Metal/HVAC Pro Calc calculator remains under warranty before calling or returning any device for evaluation or repairs. 2. If your calculator won't turn on, try pressing the Reset button first. If it still won't turn on, check the batteries as outlined in the User's Guide. 3. If there is a black spot on the LCD screen, THIS IS NOT A WARRANTY DEFECT.
WARRANTY Warranty Repair Service – U.S.A. Calculated Industries (“CI”) warrants this product against defects in materials and workmanship for a period of one (1) year from the date of original consumer purchase in the U.S. If a defect exists during the warranty period, CI at its option will either repair (using new or remanufactured parts) or replace (with a new or remanufactured calculator) the product at no charge.
INCIDENTAL, OR CONSEQUENTIAL DAMAGES RESULTING FROM ANY DEFECT IN THE PRODUCT OR ITS DOCUMENTATION. The warranty, disclaimer, and remedies set forth above are exclusive and replace all others, oral or written, expressed or implied. No CI dealer, agent, or employee is authorized to make any modification, extension, or addition to this warranty.
INDEX Accessing Preference Settings, 111 ACCURACY, AUTO SHUT-OFF, BATTERIES, ERRORS (APPENDIX I), 114 Accuracy/Errors, 114 Adding and Subtracting Fractions of an Inch, 35 Adding Dimensions, 29 Adding Linear Measurements, 34 Angle and Diagonal (Hypotenuse), 88 Arc Calculations — Arc Length and Diameter Known, 79 ARC/CIRCLE EXAMPLES, 78 Arched/Circular Rake-Walls — Chord Length and Segment Rise Known, 80 Arched Windows, 81 Arc Length — Degree and Diameter Known, 78 Arc Length — Degree and Radius Known, 78 AR
Degree of Pitch, 86 Dividing Dimensions, 29 Dividing Offset into Multiple Degreed Elbows for Manageable Sections, 51 D:M:S EXAMPLE, 45 ENTERING DIMENSIONS, 25 Entering Linear Dimensions, 25 Entering Square/Cubic Dimensions, 25 EXAMPLES — USING THE SHEET METAL/HVAC PRO, 33 Fan Law 1, 75 Fan Law 2, 76 Fan Law 3, 77 FAN LAW EXAMPLES, 75 FAN LAW FORMULAS (APPENDIX E), 106 FAN LAW KEYS, 14 FEET-INCH-FRACTION and METRIC KEYS, 8 Field Measuring for Ductwork Using the Law of Cosines Introduction, 55 Finding “Angle
Reset Key, 115 RIGHT TRIANGLE and ROOF FRAMING EXAMPLES, 84 Rise, 88 Rise and Diagonal, 88 Roof Framing Definitions, 84 Scientific Notation, 39 Setting Fixed/Constant Fractional Resolution, 24 SETTING FRACTIONAL RESOLUTION, 23 Setting Fraction Resolution to Other Than 16ths — Using the Preference Setting Mode, 23 Sheathing Cut, 89 Sheet Metal Panels for an Irregular Hip Roof, 59 Square Area (x2), 36 Square Conversions, 28 Squaring-up a Foundation, 82 STAIR KEY, 19 Stair Layout Definitions, 94 STAIR LAYOUT E
Designed in the United States of America 01/21 UG4090E-D
