| SPECIAL menu
The calculator has an RPN function with addition, subtraction, multiplication, and division (which should be familiar to users of HP desk calculators). Note that you should use the underline key (_) instead of the minus key (-) for subtraction (this is because the minus key is assumed to indicate a negative number, not subtraction).
• EXPRESSION EVALUATOR... This routine lets you write a mathematical expression, enter numeric values for the expression variables, and have the computer solve it for X and (optionally) Y values. The program parses the expression into components and performs the operations.
The expression evaluator understands the following symbols (upper or lower case entries are OK):
Some general considerations:
|The underlying code for the expression evaluator was developed by the late, great Robert Purves (deceased a few years ago, and greatly missed by the FB community). I 'borrowed' it -- with his permission -- and made some modifications for LabHelper. But Robert P. deserves all the creative credit.|
Note that due to rounding errors, the calculations are not 100% reversible (e.g. computing the pressure at a given altitude and then using that computed pressure to calculate altitude will not yield the identical initial altitude -- but it will be very close).
In the example at right, pressure is sea level standard atmospheric pressure(760 torr), temperature is the typical mammalian body temperature (37 °C), etc. Note that at this temperature the saturation vapor pressure of water is about 47.6 torr (this is not affected by the total pressure in the system).
Other considerations for this calculator:
In the example at right, pressure is sea level standard atmospheric pressure (760 torr), temperature 10 °C, the water is fully saturated with oxygen, and there are 2 parts/thousand of dissolved solutes (reasonable for fairly fresh water). The calculator provides the dissolved oxygen per unit volume, and for the total volume.
The initial popup menu contains some very generalized equations, and also allows you to switch to submenus for specific taxa (arthropods, fish, birds, mammals, etc.). For most taxa, several different equations are available (from different literature sources, which are described in the 'help' field to the right). You can also pick the desired output units. The energy equivalence of metabolism (joules per ml of oxygen consumed) is set at 20.1 joules/ml (this varies -- but not by very much -- with different metabolic fuels). The mass coefficient in the allometric equation ('a' value) is adjusted to reflect whatever output unit is in use. Results can be stored for later use. Metabolism for all taxa are calculated from power functions:
metabolism = a Mb
(where a is the mass coefficient, M is mass, and b is the mass exponent)
This example shows an estimate of the resting metabolic rate (RMR) of
a 37.3 g bird, in units of ml O2/min.
The equation was derived from a paper published by Andrew Mckechnie and
Blair Wolf (Click here for a list of the references from which allometric equations were obtained.).
You can also adjust the activity intensity for the animal, ranging from inactive (minimal metabolism; MMR) to average daily metabolism (3 X MMR)to very vigorous activity -- up to 100X MMR, which is reasonable for some large flying insects.
This window calculates the washout rates of theoretical perfectly-mixed chambers as a function of volume and flow rate. The computed value is the time for X% of intial gas volume to be replaced -- akin to the 'half-life' concept for radioactive decay and related phenomena. Note that no real chamber will exactly match these estimates.
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If you measure only one of these two gas species, the program will use RQ to estimate the other. If you measure both O2 and CO2 concentration changes, the program will optionally use O2 in the calculation of VCO2.
NOTE: it is assumed that sample gas is dried before measurement, and the default settings are:
If you measure only one of these two gas species, the program will use RQ to estimate the other. If you measure both O2 and CO2 concentration changes, the program will optionally use O2 in the calculation of VCO2. NOTE: it is assumed that sample gas is dried before measurement, and the default settings are:
NOTE: The program expects latitude and longitude in fractional degrees, not degrees and minutes. Thus 27° 30’ north should be entered as ’27.5’ (i.e., halfway between 27° N and 28° N).
Sun time estimates are approximate for several reasons:
• Sunrise and sunset times are based on local solar noon (i.e., when the sun is at its zenith (highest above the horizon) from the perspective of the observer’s position. This is likely to be slightly different from local time. As defined by people, time zones are arbitrary, and since they are roughly 15 ° of longitude wide and often do not run strictly north and south, sunrise and sunset times can vary by an hour or more with a single time zone.NOTE: The U.S. Naval Observatory hosts a web page (USNO Sun and Moon Data) that permits very accurate calculations of solar and lunar data. It incorporates ‘fixes’ for many of the issues described above, and — if you are connected to the internet — can be accessed with the ‘Naval Observatory Website’ button.
• The 'Get Latitude and Longitude From World Map' button opens a window with a world map (d'oh!) in Mercator projection. Move the cursor to the desired location and hit either the spacebar or return keys to select that position; as you move the cursor the latitude and longitude boxes at upper left update continuously. If you want to select a position on a higher-resolution 'regional' map, click the Zoom in X5 button, a rectangular cursor appears; move it until it encloses your area of interest and hit either the spacebar or return keys to enlarge that region. Then use the cursor and keys to select a position as described above.
Location data are accurate only to 0.33 degree of longitude and 0.25 degree of latitude on the world map and 0.11 degrees of longitude and latitude on the regional maps, but that should be accurate enough for most sunrise-sunset calculations.
As geographic references, the maps show the equator (yellow), the Prime or Greenwich Meridian (zero degrees of longitude), the Arctic and Antarctic Circles (~ 66.5 degrees N and S), and the Tropics of Cancer and Capricorn (~ 23.3 degrees N and S). Only a few of these will be visible on the enlarged regional maps.
Of course, if you want higher-resolution position data (and you are connected to the Internet), use Google Earth.
• The 'Annual Plot' button will compute and display an entire year's day length cycle, based on latitude-longitude position. The 'Print Data to Spreadsheet' button makes a tab-delineated .xls spreadsheet containing the annual cycle (date, sunrise time, sunset time, and day length). This example shows a Polar-region cycle, with complete darkness in winter and 24-hour sunlight in summer: