I do not see any problems with your equations other than a possible loss of precision by basing your original gravity calculation on your pre-boil calculation.
If you are adding sugar, then you may need to perform real-world tests to calibrate your sugar potential values.
Are your final values calculated along the lines?
gravity_points(gravity) = gravity - 1 * 1,000
gravity_points_contributed_by_sugars = for each sugar in sugar_additions, sum(sugar.weight * sugar.gravity_points)
total_grain_potential_in_points = for each grain in grist, sum(grain.weight * grain.gravity_points)
efficiency_percentage = (volume_in_gallons * gravity_points(measured_gravity) - gravity_points_contributed_by_sugars) / total_grain_potential_in_points * 100
With that said, it is not uncommon for actual values to be off because the predicated efficiency was optimistic or one's hypothetical potential values are not accurate. Additionally, it is possible that one's actual extraction efficiency is less than the calculated value due to using hypothetical grain potential values that are too low for the actual grain in use. Extraction efficiency should not vary with grist because extraction efficiency is a unit of measure with respect to process and plant. If one obtains 77% efficiency with Briess 2-row and 80% efficiency with Avangard Pils, it should raise a red flag that the hypothetical grain extract potential values used in the calculation may not be accurate. For this very reason, I stick with points per pound per gallon (PPG) as my extraction unit of measure.
points_per_pound_per_gallon = gravity_points(measured_gravity) * volume_in_gallons / grist_weight_in_pounds
The beauty PPG is that it is an easily scaled metric.
For example, here's the grist that I used last weekend
10lbs Avangard Pils
0.5lb Briess CaraPils
0.5lb Torrified Wheat
My O.G. was 1.064, and my total final liquid volume minus the hops and break was 5.5 gallons (it's important to separate the liquid from the hops and break material after casting out, so that one can measure its volume). My cast-out volume was 5.25 gallons. I left 0.25 gallons with the break and hops. What was my PPG extraction rate?
ppg_extraction_rate = gravity_points(1.064) * 5.5 / 11 = 32 points per pound per gallon, mixed grist
I have used Avangard Pils enough to know ahead of time that I was more than likely going to obtain an extraction rate of 32 points per pound because the high percentage of pils malt swamps out the contributions by the carapils and torrified wheat.
Now, with a PPG value for a grist that is roughly 90% +/- 1% Avangard Pils, I can calculate the amount of grist needed for any gravity and any volume.
For example, let's figure out how many pounds of a 90% +/- 1% Avangard Pils grist is needed to hit 1.053 with a final kettle volume of 11 gallons.
pounds_of_grist = gravity_points(1.053) * 11 / 32 = ~18.22 pounds
pounds_of_avangard_pils = 18.22 * 0.91 = 16.58 pounds
pounds_of_carapils = 18.22 * 0.045 = 0.82 pounds
pounds_of_torrified_wheat = 18.22 * 45 = 0.82 pounds
One way to look at PPG versus extraction efficiency percentage is that working with PPG is like working with a transfer function versus working with its differential equation equivalent.
Topic: Pre-Boil Gravity Calculations (Read 2430 times)
