RPN-65 - An HP-65 Simulator for iOS

Program Library 2 for RPN-65

Please note:
For copyright reasons, program documentation is not available for download. User's manuals in PDF format
for all HP programs listed below are available from The Museum of HP Calculators.

Manuals are highly recommended for:
  • detailed program descriptions
  • illustrations
  • equations used in the calculations
  • step-by-step instructions
  • additional examples.

See section "Sharing" to learn how to load cards.

Quick Links

Aviation 1	Chemical Engineering 1	Electrical Engineering 2	Finance 1

Machine Design 1	Navigation 1	Statistics 2	Surveying 1

HP Aviation Pac 1
01 - Aircraft Flight Plan with Wind	This program is used when making a flight plan which includes winds. It solves the wind triangle, giving correct values for airplane heading and ground speed.
02 - Flight Management	This program calculates either time flown, distance flown or ground speed using the other two variables as inputs.
03 - Predicting Freezing Levels	The program computes the theoretical freezing level in feet above mean sea level, from altitude and temperatures.
04 - General Aircraft Weight and Balance	The program calculates the final values of gross weight and moment or gross weight and center of gravity that are used to determine your position in the weight-balance envelope furnished with your aircraft.
05 - Customized Weight and Balance	The weight and balance of a two-or four-place light aircraft are easily calculated using this program and a constant card.
06 - Turn Performance	This program calculates the G-force, turn diameter, time required to complete a 3600 turn, and stall speed for an airplane as a function of an aircraft's bank angle, airspeed and normal stall speed.
07 - Rate of Climb and Descent	The inputs of this program are true airspeed (TAS), elevation change (∆ ALT), and either rate-of-climb (ROC) or the distance (DIST) over which the elevation change is to occur.
08 - Head Winds and Cross Winds	This program calculates both the head wind and cross wind components from the aircraft heading and reported winds.
09 - Flight Planning and Flight Verification	This program can be used for flight planning and updating the flight plan as it is being flown.
10 - Determining In-Flight Winds	This program computes the winds at altitude from TAS, course of aircraft, ground speed and heading.
11 - Standard Atmosphere	This two card program can be used to estimate atmospheric conditions from pressure altitude.
12 - Mach Number and True Airspeed	This program converts calibrated airspeed (CAS) to mach number and true airspeed (TAS).
13 - True Air Temperature and Density Altitude	This program accounts for the compressibility effects of high speed flight.
14 - Lowest Usable Flight Level	This program computes the lowest usable flight level for aircraft flying above 18,000 feet mean sea level from the current altimeter setting.
15 - Great Circle Plotting	Given the latitude and longitude of two points on the globe and an intermediate longitude, this program calculates the latitude corresponding to the intersection of the great circle route and the intermediate longitude.
16 - Rhumbline Navigation	This program accepts the coordinates of two points on the globe and calculates the rhumbline heading and distance between them.
17 - Great Circle Navigation	This program computes the great circle distance between two points and computes the initial heading from the first point.
18 - Position Given Heading, Speed, and Time	Given the starting position, the heading, the speed and the time of travel, the destination position is calculated by a rhumbline.
19 - Line of Sight Distance	This program calculates either the aircraft altitude or the line-of-sight distance from an aircraft to a transmitting station.
20 - Position by Two VORs	This program finds the distance from one of two VOR's to an aircraft.
21 - Navigation by Two VORs	This program may be used to navigate between any two points provided signals can be received from two VOR stations.
22 - Position by One VOR	This program computes the distance from a VOR station to an aircraft.
23 - DME Speed Correction	The program calculates ground speed from the DME speed indicator when the airplane course is not directly to or from a DME station.
24 - Average Wind Vector	When planning a flight it may be helpful to reduce several reported wind vectors along the flight path to one average wind.
25 - Course Correction	The program calculates the new corrected heading and the distance to destination for an aircraft which has strayed a known distance off course.
26 - Time of Sunrise/Sunset	This program calculates time of sunrise and sunset given the observer's longitude and latitude.
27 - Azimuth of Sunrise and Sunset	This program computes the true heading (azimuth) of the sun as it rises or sets. Input data are day of the month, month of the year and latitude.
28 - Pilot Unit Conversions	This program performs unit conversions commonly encountered by pilots. Included are conversions between Fahrenheit and Celsius degrees, statute miles and nautical miles, liters and gallons, and gallons of gasoline and pounds of gasoline.
29 - Customized Unit Conversions	With this program, a pilot can permanently record his most used conversion factors and easily perform unit conversions.

HP Chemical Engineering Pac 1
01 - Ideal Gas Equation of State	This program provides an interchangeable solution between the five variables of the ideal gas law.
02 - Redlich-Kwong Equation of State	The Redlich-Kwong equation is a two constant equation of state which takes some of the adverse properties of real gases into account. It is generally a better approximation of the behavior of real gases than either the ideal gas law or van der Waals' equation.
03 - Reversible Polytropic Process for an Ideal Gas	This program may be used to solve interchangeably between pressure ratio, volume ratio, temperature ratio, and density ratio for polytropic processes involving ideal gases.
04 - Isentropic Flow for Ideal Gases	These two cards replace isentropic flow tables for a specified specific heat ratio k.
05 - One Dimensional Normal Shocks for Ideal Gases	This card replaces one dimensional normal shock tables for a specified specific heat ratio k.
06 - Fluid Transport Numbers	It is common practice in the fields of heat, mass, and momentum transfer to lump the many variables involved into dimensionless groups. These dimensionless groups, or fluid transport numbers, greatly simplify correlating experimental data and handling calculations once correlations have been obtained.
07 - Fanning Friction Factor and Conduit Flow	These cards may be used to solve a variety of problems involving viscous conduit flow.
08 - Conservation of Energy	These cards convert kinetic energy, potential energy and pressure-volume work to energy.
09 - von Kármán Analogy for Heat and Mass Transfer	The von Kármán analogy forms a link between momentum, heat, and mass transfer for conduit flow.
10 - Heat Exchanger Analysis	This set of cards allows analysis of heat exchangers. Cards 1 and 2 are of general applicability. They use heat balance techniques to evaluate effectiveness, heat transfer and outlet temperatures. The remaining cards are configuration cards for particular types of heat exchangers.
11 - Heat Transfer Through Composite Cylinders and Walls	This program can be used to calculate the overall heat transfer coefficient for composite tubes and walls from individual section conductances and surface coefficients.
12 - Straight Fin Efficiency	This program evaluates fm efficiency. Given the number of fins per unit of surface length and the temperature difference, the total heat transfer can also be found.
13 - Natural Convection	These three cards can be used to estimate convective heat transfer coefficients for isothermal vertical walls, vertical cylinders, horizontal cylinders and flat plates.
14 - Black Body Thermal Radiation	This program can be used for various calculations involving black body radiation.
15 - Temperature or Concentration Profile for a Semi-infinite Solid	This program solves physical situations in heat and mass transfer by assuming an infinite geometry.
16 - Hydrocarbon Combustion	Given the atomic composition of a hydrocarbon fuel and the desired amount of excess air, the air-fuel ratio on a mass and mole basis is found. The number of moles of products is also calculated along with the volume percents of sulfur dioxide, carbon dioxide, water vapor, oxygen and nitrogen. Complete combustion is assumed.
17 - Curve Fitting	These three cards can be used to fit experimental data to straight lines, exponential curves, and power curves.
18 - Unit Conversions	These two cards convert interchangeably between commonly used units of pressure and energy.

HP E.E. Pac 2
01 - Mismatch Error Limits	This program computes uncertainty of power transfer and maximum phase error in a mismatched microwave circuit.
02 - Multiple Mismatch Error Limits	When a device is inserted between a source and load in a simple insertion-loss measurement scheme, mismatch error due to secondary reflections may be calculated. This program computes the maximum and minimum error values.
03 - Smith Chart: Radially Scaled Parameters	The distance between a point on a Smith Chart and its center may be measured by a number of parameters. Some of the most commonly used ones are standing wave ratio, reflection coefficient, return loss, and mismatch loss.
04 - Smith Chart: Impedance ⇄ Reflection Coefficient	Any point on a Smith Chart may be referenced in a number of different coordinates. This program converts between impedance and reflection coefficient.
05 - Microstrip Calculations Rev. Oct 20, 2015	This program is composed of three cards. The first one accepts conductor width w, dielectric thickness h, and relative permittivity ε_r, and computes relative phase velocity V_r and characteristic impedance Z_c for lossless line.
06 - Transmission Line Calculations	This program computes the input impedance of lossy transmission line terminated in Z_L.
07 - Cutoff Frequency in Coax	This program provides an interchangeable solution to the coax cutoff equation.
08 - Rectangular Waveguide Calculations	This program computes the cutoff frequency of energy propagating in the TE_mn mode in waveguide of dimensions a x b filled with a dielectric of relative permittivity ε_r.
09 - Frequency Conversion	This program allows conversion among various representations of frequency.
10 - Line and Pulse Spectrum Analysis	This program accepts and stores the spectrum analyzer display setting (MHz/cm). Lobewidth is then converted to pulse width and linespacing is converted to pulse spacing. The displayed voltage is now converted to the RMS voltage of the pulse and the peak-to-average power ratio is displayed in decibels.
11 - Spurious Responses	Nonlinear elements are often used to mix RF and LO signals to produce an IF signal. The mixer may also output frequencies formed from harmonics of the inputs. This program computes values M and N which produce spurious responses falling within some specified IF band.
12 - FM Sideband Levels	This program computes sideband level in dB with respect to the level of either the modulated or unmodulated carrier. Inputs are sideband number and either modulation index or peak phase deviation in degrees.
13 - Modulation Index for Specified Carrier Suppression	This program computes a value of modulation index which causes a specified amount of carrier suppression.
14 - Constant-Excess Noise Measurement	A commonly used method of determining a receiver's noise figure is the constant-excess or Y-factor noise measurement technique. For a given T_c, T_h, and Y this program computes noise figure F.
15 - Noise Figure of Cascaded Networks	This program accepts noise figure and gain, both expressed in dB, of an arbitrary number of networks and computes the overall noise figure in dB.
16 - Impedance Matching	This program accepts complex load and source impedances in rectangular form and will output all possible solutions of L-networks to transform one impedance into the other.
17 - Unilateral Design: Figure of Merit, Maximum Unilateral Gain	This program assists in designing a transistor amplifier with the aid of s-parameters.
18 - Unilateral Design: Gain Circles	This program calculates transducer power gain and constant gain circles.
19 - Unilateral Design: Noise Figure Circle	This program computes the location and radius of a circle on a Smith chart which defines the values of source reflection coefficient which will produce a noise figure F_i.
20 - Bilateral Design: Stability Factor, Maximum Gain, Optimum Matching	This program may be used to compute the maximum gain available and the load and source reflection coefficients which yield the maximum gain. This program computes the center and the radius.
21 - Bilateral Design: Gain Circles	If it is desired to build an amplifier having gain less than the maximum possible for the transistor to be used, a gain circle is constructed.
22 - Bilateral Design: Stability Circles	This program computes the centers and the radii of stability circles.
23 - Load and Source Mapping	This program computes the source or load reflection coefficient from the corresponding load or source reflection coefficient.
24 - Linear and Langrangian Interpolation	This program performs linear interpolation or evaluates the Langrangian interpolating polynomial P₂(x) of degree two.
25 - Parameter Conversion: S⇄Y, Z, G, H	Two-port s-parameters may be converted to and from any of Y-, Z-, G-, or H-parameters using a single matrix equation.
26 - Parameter Conversion: S⇄T	These two programs allow interconversion of scattering parameters and transmission parameters.
27 - Complex Matrix Operations	These two cards will either multiply or add 2 x 2 complex matrices.

HP Finance Pac 1
01 - Compound Amount	Given values for any three of the four variables (n, i(%), PV or FV) this program will calculate a value for the remaining variable.
02 - Direct reduction loan; solve n, PMT, or PV	Given the periodic interest rate (i) and values for two other variables (n, PMT, or PV) this program will calculate a value for the remaining variable.
03 - Direct reduction loan; solve for i	This program calculates the periodic interest rate (i) given values for the other three variables (n, PMT, PV).
04 - Direct reduction loan with balloon payment; solve for n, PMT, PV, or BAL	Given the periodic interest rate (i) and values for three other variables (n, PMT, PV or BAL) this program will calculate a value for the remaining variable.
05 - Direct reduction loan with balloon payment; solve for i	This program will calculate the periodic interest rate (i) given values for the other four variables (n, PMT, PV, and BAL).
06 - Sinking fund; solve for n, PMT or FV	Given the periodic interest rate (i) and values for two other variables (n, PMT, or FV) this program will calculate a value for the remaining variable.
07 - Sinking fund; solve for i	This program will calculate the periodic interest rate (i) given values for the other three variables (n, PMT, and FV).
08 - Periodic savings, annuity due; solve for n, PMT, or FV	Given the periodic interest rate (i) and values for two other variables (n, PMT, or FV) this program will calculate a value for the remaining variable.
09 - Periodic savings, annuity due; solve for i	This program calculates the periodic interest rate (i) given values for the other three variables (n, PMT, and FV).
10 - Present value, annuity due; solve for n, PMT, or PV	Given the periodic interest rate (i) and values for two other variables (n, PMT, or PV) this program will calculate a value for the remaining variable.
11 - Present value, annuity due; solve for i	This program will calculate the periodic interest rate (i) given values for the other three variables (n, PMT, and PV).
12 - Present value, annuity due with balloon payment; solve for n, PMT, PV, or BAL	Given the periodic interest rate (i) and values for three other variables (n, PMT, PV, or BAL) this program will calculate a value for the remaining variable.
13 - Present value, annuity due with balloon payment; solve for i	This program will calculate the periodic interest rate (i) given values for the other four variables (n, PMT, PV and BAL).
14 - Savings – compounding periods different from payment periods	Payments into a savings plan may not occur with the same frequency as the compounding frequency offered. This program solves for either the periodic payment amount (given future value) or future value (given the payment amount).
15 - Nominal to effective/effective to nominal rate conversion	This card contains two independent programs. The first addresses quarterly compounding, monthly compounding, etc. The second program is for continuous compounding. Given either rate, the other can be calculated.
16 - Direct reduction loan; accumulated interest/remaining balance	This program finds both the total interest paid over a specified number of payment periods and the remaining balance at the end of the last specified period, given the periodic interest rate, periodic payment amount, loan amount, and the beginning and ending payment numbers for the time span being considered.
17 - Direct reduction loan; amortization schedule	Given the periodic interest rate, periodic payment amount, loan amount and payment number this program will generate the values for a loan amortization schedule, starting with the payment number.
18 - Add-on rate installment loan	This program calculates the monthly payment amount, total finance charge, and the Annual Percentage Rate (APR) for an add-on rate loan.
19 - Constant payment to principal loan amortization schedule	This type of loan is structured such that the principal is repaid in equal installments with the interest paid in addition. Therefore each periodic payment is different; it has a constant amount applied toward the principal and a decreasing amount towards interest.
20 - Interest rebate – Rule of 78's	This program calculates the unearned interest (rebate) as well as the remaining principal balance due for a prepaid consumer loan using the rule of 78's.
21 - Internal rate of return; up to 12 cash flows	The interest rate that equates the present value of all future cash flows with the original investment is known as the internal rate of return. Given the initial investment and up to 12 cash flows, this program calculates the periodic IRR.
22 - Internal rate of return; up to 7 cash flows	This program also calculates the periodic rate of return that will equate an initial investment to the present value of all future cash flows. By limiting the maximum number of cash flows to 7, this program is able to calculate answers more quickly and more accurately (±.001%) than program 21.
23 - Discounted cash flow analysis – Net present value	Assuming a minimum desired yield (cost of capital, discount rate), this program finds the present value of the future cash flows generated by the investment and subtracts the initial investment from this amount.
24 - Straight line depreciation schedule	The annual depreciation allowance using this method is determined by dividing the cost or other basis of valuation (starting book value) less its estimated salvage value by its useful life expectancy.
25 - Sum-of-the-years' digits depreciation schedule	The sum-of-the-years' digits method is an accelerated form of depreciation, allowing more depreciation in the early years of an asset's life than allowed under the straight line method.
26 - Variable rate declining balance depreciation schedule	The variable rate declining balance method is another form of accelerated depreciation; as such it provides for more depreciation in earlier years and decreasing depreciation in later years.
27 - Crossover point – Declining balance to straight line	As indicated in the description and example for program 26, the declining balance method of depreciation may not fully depreciate an asset in the asset's lifetime. In these circumstances there is an optimum point in the useful life where a switch from the declining balance method to the straight line method should be made. This is the "crossover point".
28 - Days between dates (actual)	This program calculates the actual number of days between any two dates that occur between January 1, 1901 and December 31, 2099.
29 - Days between dates (30/360 basis)	This program calculates the number of days between any two dates on a 30/360 basis (30 day month, 360 day year), as is the custom for many securities.
30 - Bond price	This program calculates the "flat" price (i.e., not including accrued interest) of a semiannual coupon bond.
31 - Bond yield (one or more remaining coupon periods)	This program calculates the annual yield of a semiannual coupon bond when there are one or more remaining coupon periods between settlement and redemption dates.
32 - Bond yield (less than one remaining coupon period)	This program calculates the annual yield of a semiannual coupon bond when there is less than one coupon period remaining between settlement and redemption dates.
33 - Accrued simple interest	This program calculates the accrued simple interest given the number of days, annual interest rate, and the initial principal. Answers based on a 360 or 365 day year are made available.
34 - Linear regression (trend line)	This program performs a least squares linear regression given a series of x,y data pairs as input.
35 - Exponential curve fit (growth curve)	Given a series of x,y data pairs as input this program performs a least squares regression to determine the best exponential curve fit of the form y = b·e^mx.
36 - Total, average, and percent of total (up to 8 items	This program computes a total for up to 8 items, calculates each item's percent of the total and determines the average value of all items entered.
37 - Moving averages	This program calculates a 2 to 6 unit moving average.
38 - Invoicing	Given a discount rate, number of units, and price per unit for each line item, this program calculates the net line total, and maintains a running subtotal and grand total.

HP Machine Design Pac 1

Dynamics
01 - Constant Acceleration – Time	This program calculates an interchangeable solution among the variables displacement, acceleration, initial velocity, and time, for an object that undergoes constant acceleration. The motion may be either circular or linear.
02 - Constant Acceleration – Velocity	This program calculates an interchangeable solution among the variables displacement, acceleration, initial velocity, and fmal velocity, for an object undergoing constant acceleration. The motion may be either circular or linear.
03 - Kinetic Energy	This program calculates an interchangeable solution among the variables weight (or mass), velocity, and kinetic energy, for an object moving at constant velocity. The program operates in either English or metric units.

Vibrations
04 - Free Vibrations	This program provides an exact solution to the differential equation for a damped oscillator vibrating freely: mẍ + cx + kx = 0
05 - Vibration Forced By F₀·cosωt	This program finds the steady-state solution for an object undergoing damped forced oscillations from a periodic external force of the form F₀·cosωt. The differential equation to be solved is mẍ + cẋ + kx = 0.
06 - Forced Oscillator With Arbitrary Function	This program determines the displacement x, velocity ẋ, and acceleration ẍ of a damped oscillating mass m that is being driven by some forcing function f. A numerical solution is computed for the nonhomogeneous differential equation mẍ + cẋ + kx = f(t).
07 - Fourier Series	This program computes the Fourier coefficients from discrete versions of the Fourier series formulas given a large enough number of samples of a periodic function.
08 - Critical Shaft Speed	Suppose a rotating shaft is simply supported at both ends and has a series of n weights attached. Then there are critical speeds at which the shaft will become dynamically unstable. This program finds the fundamental critical speed.

Linkages
09 - Four Bar Function Generator	These programs may be used to design a four bar linkage which will approximate an arbitrary function of one variable. Freudenstein's approach is used in the solution. The second card of the three can be used independently to solve 3 x 3 linear systems.
10 - Progression of Four Bar System	These two cards calculate the position, angular velocity, and angular acceleration of both the connecting and output links of a four bar mechanism, given the same values for the input link.
11 - Linear Progression of Slider Crank	This program computes the displacement, velocity, and acceleration of the slider in a slider crank mechanism, (e.g. the piston wrist-pin in an internal combustion engine) given crank radius, connecting rod length, slider offset, crankshaft speed, and crank position. The maximum and minimum displacements and the stroke are also calculated.
12 - Angular Progression of Slider Crank	This program computes the connecting rod angle, velocity, and acceleration in a slider crank mechanism (e.g. the connecting rod in an internal combustion engine), given crank radius, connecting rod length, slider offset, crankshaft speed and crank position. The maximum and minimum angular values for Φ and the total angular throw of the connecting rod are also calculated.

Cams
13 - Cam Data Storage	This program stores the cam data for programs 14 through 18 in this Pac.
14 - Harmonic Cam Design – Radial Roller Follower	This program computes the parameters necessary for the design of a harmonic circular cam with radial roller or point follower.
15 - Harmonic Cam Design – Flat Faced Roller Follower	This program computes the parameters necessary for the design of a cam with radial flat-faced follower.
16 - Roller Follower Cam Function Generator	This program generates roller follower circular cam data for an arbitrary function. The user specifies the follower function and its derivative by keying them in memory. Values are then calculated for grinding the cam.
17 - Flat Faced Follower Cam Function Generator	This program generates flat faced follower circular cam data for an arbitrary function. The user specifies the follower function and its derivative by keying them in memory. Values are then calculated for grinding the cam.
18 - Linear Cam Function Generator	This program generates roller or point follower cam data for an arbitrary function on a linear cam. The user specifies the followerfunction and its derivative by keying them in memory. Values are then calculated for the cam profile, pitch curve (or roller path) and grinder path.

Gears
19 - Spur Gear Reduction Drive	For a spur gear meshing with a pinion, this program performs an interchangeable solution among the variables reduction, distance between the centers, diametral pitch, and number of pinion teeth.
20 - Standard External Involute Spur Gears	This program uses two cards to compute various parameters for standard external involute spur gears.
21 - Spur/Helical Gear Forces	This program computes the various forces that act on spur and helical gears as a result of the gear torque.
22 - Bevel Gear Forces	This program computes the forces that act on straight or spiral bevel gears as a result of the torque.
23 - Worm Gear Forces	This program computes the forces acting on a worm and worm gear in mesh as a result of the input torque.

Springs
24 - Spring Constant	This program calculates the value of any variable given the other four in the spring equation. It may be used to solve any general linear equation of the form y - y₀ = m(x - x₀). It is also useful for linear interpolation in tables.
25 - Helical Spring Design	This program interchangeably computes deflection, stress, and load for round-wire helical compression and extension springs.
26 - Torsion Spring Design	This program interchangeably computes deflection, stress, and load for round and flat wire torsion springs.
27 - Flat Spring Design	This program computes the load and stress given deflection for eight cases of flat springs, including multiple leaf triangular plate springs.

Power Transmission
28 - Cone and Plate Clutches	This program computes the torque and horsepower capacity for cone and plate clutches assuming either uniform wear or uniform pressure.
29 - Power Screws	This program computes the load that may be raised or lowered by some torque, or the torque necessary to raise or lower some load, by a power screw. It also computes the efficiency of the screw and the minimum thread coefficient of friction to prevent overhauling.
30 - RPM/Torque/Power	This program provides an interchangeable solution for RPM, torque, and power in both Système International (metric) and English units.

Machine Geometries
31 - Line – Line Intersection/Grid Points	This card calculates the point of intersection of two lines and the cartesian coordinates of points in other coordinate systems.
32 - Circle-Line Intersection	This program computes the points of intersection of a line and a circle, given the circle center coordinates and radius, and either two points on the line or one point and angle to the line from the horizontal axis.
33 - Circle-Circle Intersection	This program calculates the coordinates of the points of intersection for two circles, given the radius and center coordinates for each.
34 - Points On A Circle	This program calculates coordinates on a circle at regular angular increments, or evenly spaced over the entire circle.
35 - Belt Length	This program computes the belt length around an arbitrary set of pulleys. It may also be used to compute the total length between any connected set of coordinates.

HP Navigation Pac 1

Piloting and Dead Reckoning
01 - Length Conversions	This program converts between various measures of length, metres, feet, fathoms, nautical miles, and statute miles.
02 - Speed, Time, and Distance	This program finds a value for speed, time or distance when the other two are specified.
03 - Time-Arc Conversion	This program converts among arc and various representations for time.
04 - Propeller Slip	This program calculates a value for RPM, pitch, slip, or speed when the other three are specified.
05 - Fuel Consumption	This program solves for fuel consumption, speed, or distance run given the other two.
06 - Distance to or Beyond Horizon	This program computes the distance to an object of known height whose base is obscured by the horizon and whose top subtends a given sextant altitude with the horizon.
07 - Distance by Horizon Angle and Distance Short of Horizon	This program calculates the distance between an observer and an object when (1) the vertical angle between its waterline and the horizon has been observed from a known height of eye or (2) the object's height is known, together with its subtended angle.
08 - Dead Reckoning	This program calculates a ship's DR position given the ship's course, speed, and elapsed time from the last fix or DR position.
09 - Rhumbline Navigation	This program accepts the coordinates of two points on the globe and calculates the rhumbline course and distance between them.
10 - Great Circle Navigation	This program computes the great circle distance between two points and computes the initial heading from the first point.
11 - Great Circle Computation	This program computes the latitude corresponding to a specified longitude on a great circle passing through two given points.
12 - Composite Sailing	This program computes, for each of two points, the longitude at which a great circle through the point is tangent to some limiting parallel.

Celestial Navigation
13 - Sextant Altitude Corrections	This set of programs is used to correct sextant readings. The first card applies index correction, height of eye correction, and mean refraction correction. The second card corrccts for sea-air temperature difference and abnormal air temperature and pressure. The third card allows almanac entries for semi-diameter of sun and moon and corrects for geocentric parallax (moon only).
14 - Long-Term Aries Almanac	This set of programs is used to compute the Greenwich Hour Angle of the first point of Aries (the vernal equinox) which is the celestial reference point from which Sidereal Hour Angle is measured.
15 - 1974-1975 Sun Almanac	This program computes the sidereal hour angle and declination of the sun and stores them for use by the Almanac Positions program. This program also computes the Equation of Time which is used with the declination by the Sunrise, Sunset, and Twilight program. The program is based on a 1974 ephemeris and will give positions with increasing error if used for other years. For 1975 no errors greater than 0.5' have been found.
16 - Sunrise, Sunset, and Twilight	This program computes the local mean time and Greenwich mean time at which the sun will be at altitude H from either horizon.
17 - Long-Term Star Almanac	This set of programs stores the position of any of 24 stars into the registers for use by the Almanac Positions program.
18 - Almanac Positions	These programs are run after the Aries Almanac and either the Sun Almanac or a star data card. They compute the position of the Sun or selected star on the celestial sphere.
19 - Sight Reduction Table	This program calculates the computed altitude and azimuth of a celestial body given the observer's latitude and the local hour angle and declination of the body.
20 - Most Probable Position	This program computes the most probable position from a single observation of a celestial object by dropping a perpendicular from the dead reckoning position to the line of position of the object.
21 - Fix by Two Observations	This program accepts the observer's dead reckoning position and intercepts and azimuths for observations of any two celestial bodies and computes the coordinates of the intersection of the lines of position of the two bodies.
22 - Fix by Three Observations	This program computes the coordinates of a fix obtained from observations of three celestial bodies.

Relative Motion Problems
23 - Distance Off an Object by Two Bearings	To determine the distance off an object as a vessel passes it, observe two bearings on the bow and note the distance run between bearings. The program calculates the distance off the object when it is abeam and at the time of the first and second bearings.
24 - Vector Addition	This program will compute the sum or difference of two vectors in polar form. It can be used to solve a large number of relative motion problems.
25 - Velocity to Change Relative Position	This program may be used when it is desired to change position relative to another vessel whose course and speed are known. The program computes the course and speed nccessary to complete the maneuver in a specified time. Bearings may be relative or true.
26 - Maneuvering Relative to Another Vessel	This program computes the course change necessary to come within distance D of a ship having known range and bearing at two different points in time.

HP Stat Pac 2

General Statistics
01 - Partial and Multiple Correlation Coefficients	The partial correlation coefficient measures the relationship between any two of the variables when all others are kept constant. Any higher order partial correlation coefficient can be computed by using this program.
02 - Moving Averages (Order 2 to 8)	Given a set of numbers, this program finds the moving averages of order n (2 ≤ n ≤ 8).
03 - Histogram (12 Intervals)	This program sorts input data into twelve intervals of equal width between specified upper and lower limits. The input data may be supplied manually or generated by a subroutine.

Distribution Functions
04 - F Distribution with Odd Degrees of Freedom	This program evaluates the integral of the F distribution.
05 - Erlang Distribution (Gamma Distribution)	This program evaluates the n-phase Erlang density function f(x) and the cumulative distribution function P(x). The mean, variance and mode are also computed.

Curve Fitting
06 - Geometric Curve Fit	This program fits a geometric curve y = ab^x to a set of data points.
07 - Gompertz Curve Fit	This program fits a Gompertz curve to a set of data points.
08 - Weibull Distribution Parameter Calculation	For a set of data, this program calculates the estimates of the Weibull parameters a and b.
09 - Weighted Regression (Special Case)	This program finds the weighted regression line for a particular case.
10 - Polynomial Approximation	This program approximates in the least squares sense the function f(x) by a polynomial of degree m, where 2 ≤ m ≤ 4.

Analysis of Variance
11 - Two Way Analysis of Variance (No Replications)	The two way analysis of variance tests the row effects and the column effects independently. This program will generate the ANOVA table for the case such that (1) each cell only has one observation and (2) the row and column effects do not interact.
12 - Two Way Analysis of Variance (With Replications)	This program generates the complete two way ANOVA table for the fixed or mixed model with interactions.
13 - Latin Square	A Latin square design is an incomplete three-way layout in which all the three factors are at the same number n of levels and observations are taken on only n² of the n³ possible combinations. The program generates the complete ANOVA table for the Latin square design.
14 - Analysis of Covariance (One Way)	The one way analysis of covariance tests the effect of one variable separately from the effect of the second variable if the second variable represents an actual measurement for each individual (rather than a category). This program will generate the complete ANOCOV table.

Test Statistics
15 - One Sample Test Statistics for the Mean	This program computes the z and the t statistics for a set of data.
16 - Test Statistics for the Correlation Coefficient	This program computes the z and the t statistics under the assumptions of normal correlation analysis for a set of data.
17 - Differences Among Proportions	This program computes a chi-square statistic for observed values of a set of independent random variables having binomial distributions.
18 - Behrens-Fisher Statistic	This program computes the Behrens-Fisher statistic for independent random samples from two normal populations having unknown means.
19 - Kruskal-Wallis Statistic	This program tests the null hypothesis that k independent random samples of varying sizes come from identical continuous populations.
20 - Mean-Square Successive Difference	This program can be used to test for randomness of samples drawn of from a population.
21 - 3 x K Contingency Table	Contingency tables can be used to test the null hypothesis that two variables are independent. This program computes the χ² statistic for testing the independence of the two variables.
22 - The Run Test for Randomness	This program tests the randomness of a sequence of symbols having two types only using a z statistic which has the standard normal distribution.
23 - Intraclass Correlation Coefficient	This program computes the intraclass correlation coefficient, a measure of the degree of association among individuals within classes or groups.
24 - Fisher's Exact Test for a 2 x 2 Contingency Table	Fisher's exact probability test is used for analyzing a 2 x 2 contingency table when the two independent samples are small in size.

Probability
25 - Probability of No Repetitions in a Sample (Birthday Problem)	Suppose a sample of size n is drawn with replacement from a population containing m different objects. Let P be the probability that there are no repetitions in the sample and Q be the probability that there is at least one repetition in the sample. This program finds P and Q for given integers m, n such that m ≥ n ≥ 1.

Quality Control
26 - x̅ and R Control Charts	For a set of samples, each having a number of data points, this program computes (1) the sample mean and the sample range, (2) the over-all mean and the average range R, (3) the upper control limit and the lower control limit for the mean, and (4) the upper control limit and the lower control limit for average range.
27 - p and c Control Charts	This program constructs a control chart for fraction defective p and a control chart for defects c.
28 - Operating Characteristic Curve (Type A)	This program uses the hypergeometric distribution to evaluate the probability P a of acceptance for a single sampling plan with finite lot size N.
29 - Operating Characteristic Curve (Type B)	This program uses the binomial distribution to evaluate the probability P of acceptance for a single sampling plan with infinite lot size (i.e., sampling from a product).

Queueing Theory
30 - Single- and Multi-Server Queues (Infinite Customers)	This program calculates a number of values for identical stations available to service calls from an infinite number of customers.
31 - Single- and Multi-Server Queues (Finite Customers)	This program is similar to program 30, but handles the case in which demand arises from a finite rather than an infinite population of customers.

HP Surveying Pac 1	Note: In most cases, examples given in this pac are heavily based on illustrations in the original HP documentation.
01 - Field Angle Traverse	This program will accept angles right, angles left, deflections right and deflections left as well as horizontal or slope distances. The coordinates of the next point are calculated, and area in square feet and acres are available upon completion of the traverse.
02 - Bearing Traverse	This program uses bearings and horizontal or slope distances to calculate coordinates.
03 - Closure for Field Angle & Bearing Traverse	This program, used in conjunction with either the Field Angle Traverse program (01), or the Bearing Traverse program (02), computes area, closure bearing and distance, total distance traversed, and precision ratio.
04 - Inverse From Coordinates	This program uses coordinates to calculate distance and bearing between points of a traverse. The area in square feet and acres, plus a summation of distance inversed are also computed.
05 - Sideshots	This program may be used alone or in conjunction with one of the traverse programs (01 or 02). Used as a stand-alone program, the reference bearing from a backsight is entered along with the coordinates of the occupied point. If used with a traverse program, these steps are omitted and data stored by a traverse program is used.
06 - Coordinate Transformation	This program translates, rotates, and rescales coordinates.
07 - Compass Rule Adjustment	(Also known as the Bowditch adjustment.) This program adjusts a traverse by the compass rule. It is intended to follow the program Closure For Field Angle and Bearing Traverses (03).
08 - Transit Rule Adjustment	This program adjusts a traverse by the transit rule method. It is intended to follow the program Closure for Field Angle or Bearing Traverses (03).
09 - Two Instrument Radial Survey	This program determines the coordinates of a point using a two instrument radial survey technique. The coordinates of the two instrument locations are entered. The bearing and distance to the target point are measured from each of the instrument locations.
10 - Curve Solution – Given ∆ & R Or ∆ & T	Given the central angle and either the radius or tangent distance, this program computes four remaining parameters plus the sector, segment and fillet areas.
11 - Curve Solution – Given R & T Or R & L	Given the radius and either the tangent or arc length, this program computes four remaining parameters plus the sector, segment and fillet areas.
12 - Curve Solution – Given ∆ & C Or R & C	Given the chord length, and either the central angle or radius, this program computes four remaining parameters plus the sector, segment and fillet areas.
13 - Elevations Along A Vertical Curve	This program computes elevation at any specified station along a vertical curve as well as the elevation at the highest or lowest point on the curve and the station at that point.
14 - Horizontal Curve Layout	Given the curve radius, the point of curvature station (P.C.) and the station on the curve, this program computes deflection angles from the tangent and long chord lengths from the point of curvature.
15 - Triangle Solution – Given SSS or SAS	This program computes the area and the unknown sides and interior angles of two cases of triangles-one which requires three sides to be known and the other which requires two sides and the included angle to be known.
16 - Triangle Solution – Given SSA	This program computes the area and the unknown sides and interior angles of a triangle in which two sides and a non-included angle are the known parameters. Both possible solutions are calculated without reentering the known parameters.
17 - Triangle Solution – Given ASA or AAS	This program computes the area and the unknown sides and interior angles of two cases of triangles-one which requires two angles and the included side and the other which requires two angles and a non-included side.
18 - Bearing Intersect	This program computes the point of intersection coordinates of two lines for which the bearing of each line is known and the coordinates of a point on each line are known.
19 - Bearing - Distance Intersect	This program calculates the coordinates of the point of intersectionof two lines-one of known bearing through known coordinates and the other of known length from a point of known coordinates. Both solutions are computed.
20 - Distance - Distance Intersect	Given two lines, each of known length and originating from two known points, this program computes the intersection coordinates.
21 - Distance From a Point To a Line	Given a point of known coordinates with a line of known bearing passing through it and a second point of known coordinates, this program calculates the offset distance from the second point to the line, the distance from the intersection to the first known point, and the coordinates of the intersection.
22 - Taping Corrections	This program will apply corrections for tension, temperature, slope, correction index and sag to yield a corrected horizontal distance as measured with a steel tape.
23 - EDM Slope Reduction – Given Zenith Angle	This program reduces slope distance to horizontal distance at the instrument elevation and at sea level and gives the difference in elevation between two stations.
24 - EDM Slope Reduction – Given ∆ Elevation	Taking into consideration the curvature of the earth, this program reduces slope distance to horizontal distance at the instrument station elevation.
25 - Field Angle Check	This program accepts a reference azimuth and field angles at each point in a traverse. The field angles are converted to bearings for each leg. At closing, the final leg is compared to the reference azimuth and the angular error of closure computed. The program can also handle traverses between two points.
26 - Stadia Reductions	This program computes the elevation of and horizontal distance to points from an instrument station using stadia methods.
27 - Three Wire Leveling	After the initial entry of the starting elevation and stadia interval factor (if it is not 100), this program uses the upper stadia hair, crosshair, and lower stadia hair readings to provide the elevation difference, elevation of final point, backsight distances and foresight distances.
28 - Slope Staking – Given Centerline Terrain Elevation	Using a previously located center line and the design cross section to provide center line terrain and hinge point elevations, this program helps in the setting of slope stakes. The program produces a distance for the rod man to move from his present trial point to a new trial point which should be very close to the catch point.
29 - Slope Staking – Given Centerline Cut/Fill	Using a previously located center line and the design cross section to provide cut or fin at center line and vertical drop from center line elevation to hinge point elevation, this program helps in the setting of slope stakes.
30 - Azimuth of the Sun	This program will yield azimuth of the sun from solar observations.
31 - Predetermined Area – Line Through a Point	This program solves one of the two cases of specifying the area of a land parcel, namely, that of hinging a side.
32 - Predetermined Area – Two Sides Parallel	This program solves one of the two cases of specifying the area of a land parcel, namely, that of sliding a side along a fixed bearing.
33 - Volume By Average End Area	This program computes end area for any station, volume from previous station, and accumulated volume to the present station.
34 - Volume of Borrow Pit	This program calculates volume of fill which can be taken from a borrow pit given grid dimensions and elevations at the grid intersections. Volume is available for each grid section and also as an accumulative volume for all previous sections.