On 2/16/07, Deane Yang <deane_yang@yahoo.com> wrote:
Ah, the dumb mathematician (me) finally gets it. The thing I never saw before is "aircraft.altitude". The point is that the different quantities (of the same dimension) come from member data of different objects, so they're all in different units. And now you want to compare or add them together.
I'd still use explicit casts to put everything into the same set of units (I like to be able to see explicitly what's going on), but I definitely have to concede that a reasonable desire is to have the conversions be done automatically and behind the scenes.
I would still prefer to write something like
if (aircraft.altitude > ground_elevation + min_agl_offset)
as
if (unit_cast<elevation_type>(aircraft.altitude) > ground_elevation + min_agl_offset)
Same here, I was only wondering aloud. In fact I hope Matthias will *only* provide the compile-time version in this first iteration.
So I know and can see easily that what units the computation takes place in. If you have a clever dimensions library that handles everything without explicit casting, then you don't know what units the computation uses. Admittedly, this is probably a misplaced worry of mine, but I can certainly envision some kind of iterative computation, where mixing the wrong units and having the library make a bad (unseen) choice of units to do the computation leads to invalid results. I have a strong aversion to hidden choices and effects like this.
Well, I have a question to Matthias concerning similar things. How does one use a unitless number? Do you use dimensionless? I posted two formulas that are from a radar handbook. The first is: h = R^2 / 2ka where h is the beam height, R is radar range, k is the refractivity (usually 4/3), and a is the Earth's radius. R and a must be the same unit, and h is returned in that unit. How would you code this using mcs::units? // Is this correct? How would I know what system's dimensionless to use? template <typename T> T radar_beam_height(T range, T earth_radius, quantity<SomeSystem::dimensionless> refractivity = quantity<SomeSystem::dimensionless>(4/3)) { const quantity<SomeSystem::dimensionless> two(2); return quantity<T>( pow(range, 2) / ( two * refractivity * range ) ); } With calling code like: // What's the radar beam height at 300 nautical miles using the mean Earth radius? quantity<SI::length> height = radar_beam_height(quantity<SI::length>(1028971200), quantity<SI::length>(6371008.7714)); The other question I have is very open-ended. An approximation for the above formula where R is given in nautical miles, and h is returned as feet is: h = (R / 1.23)^2 How would you go about implementing that with mcs::units? I have no idea what unit 1.23 is, or how they even derived that number, other than it has the Earth radius and conversion from nautical miles to feet built-in. quantity<imperial::feet> radar_beam_height(quantity<nautical::miles> range) { // This is probably not actually dimensionless, it is probably something like // nautical miles / (nautical miles * sqrt(ft)), but that seems meaningless const quantity<SomeSystem::dimensionless> c(1.23); using namespace std; return quantity<imperial::feet>(pow(range / c, 2) ); } Many thanks, --Mike