Product Spec Calc Companion. r4.0. Michael Collins.
This document is a companion to the Product Spec Calc (r4.0). It does not replace the calculator. Open the calc and this guide side by side. For each calculation the calc performs, this guide explains what the formula is doing, why each input matters, what the output is telling you, and what to do when a check fails. A student who understands why the formula works will catch a bad input. A student who just uses the calculator without that understanding will not.
Inputs & Outputs tab - rows 1 through 33
These calculations characterize the product mix and establish the operating parameters every downstream calculation depends on. Complete this section before touching the sorter or transfer tabs.
Divide carton weight in pounds by carton length in feet. Converts length to feet before dividing.
Max carton: 20 in long, 50 lbs. WT/FT = 50 / (20/12) = 50 / 1.667 = 30 lbs/ft. This value feeds roller capacity checks and incline belt calculations.
Pythagoras applied to the worst-case carton position in a curve. The carton corner must clear the outside rail.
IR = 34.5 in, Max W = 15 in, Max L = 20 in. Min Curve BF = SQRT((34.5+15)^2 + (20/2)^2) - (34.5-2) = SQRT(2450.25 + 100) - 32.5 = 50.5 - 32.5 = 18 in. Round UP to the next catalog BF. Never round down.
The maximum incline angle before the carton tips forward. The carton is modeled as tipping when its center of gravity passes its front bottom edge.
Min carton: L=9 in, H=3 in. Tumble Angle = ATAN(9 / (3x3)) x 180/PI = ATAN(1.0) x 57.3 = 45 degrees. This is the theoretical limit. Design inclines to the minimum tumble angle in the mix with a safety margin. Riverside uses 30 degrees maximum incline based on the worst case carton.
The gap between cartons after a speed change. When cartons accelerate, the gap grows. When they decelerate, it shrinks.
SpeedIn=60, SpeedOut=120, L=20 in, StartingGap=24 in. Gap = 120 x (20/60) - 20 + 24 = 40 - 20 + 24 = 44 in. The gap grew from 24 to 44 inches when speed doubled. This output feeds the sorter induction gap input.
The maximum cartons per minute achievable at a given speed and gap. Dividing by 12 converts the pitch from inches to feet to match the speed in feet per minute.
SpeedIn=60 FPM, L=20 in (max), StartingGap=24 in. Rate = 60 / ((20+24)/12) = 60 / 3.667 = 16.4 CPM. This is the design rate for the system - based on the max carton length. The min carton gives a higher theoretical rate but you design to the worst case.
Center to center distance between cartons. The simplest calculation in the sheet. Everything else derives from this.
Gap=44 in, L=20 in. Pitch = 64 in. Every 64 inches of belt carries one carton. At 120 FPM that is 120/64 x 12 = 22.5 CPM. Use pitch to sanity check your rate calculations.
Inputs & Outputs tab - rows 35 through 40
The minimum length of skewed roller conveyor needed to fully align the narrowest carton across the full belt width, while containing the longest carton during the traverse.
BF=21 in, MinW=6 in, RollerCenters=3 in, MaxL=20 in. Length = ((21-6) x 21/3 + 20) / 12 = (15 x 7 + 20) / 12 = 125/12 = 10.4 ft. Round up to next standard conveyor length.
How many seconds it takes a carton to travel a given distance at a given speed. Converts distance from inches to feet and speed from FPM to feet per second.
Scan point to sorter divert: Distance=120 in, Speed=120 FPM. Time = (120/12) / (120/60) = 10 / 2 = 5.0 seconds. The WMS has 5 seconds to respond with a sort destination after the scan fires. If confirmed WMS latency is 3 seconds, there is 2 seconds of margin. If latency is 6 seconds, the layout must change.
Sorter tab - rows 4 through 27
The sorter section is the most complex in the calculator and the most consequential in a proposal. These calculations run in sequence. Each one feeds the next. A bad input in CFPM produces a wrong Required Sorter Speed, which produces a wrong Gap Produced, which produces a wrong Pass/Fail check. Work through them in order.
The sorter calculations exist to answer one question: can this sorter run this product mix at this rate without a gap failure? If the answer is no, you have three levers: rate, speed, or sorter model. Know which one you are pulling before you go back to the customer.
The minimum belt speed needed to physically move enough cartons per minute to meet the required rate. Uses average carton length and applies a 1.15 safety factor.
Required Rate = 20 CPM, Max carton L=20 in, Safety Factor=1.15. CFPM = (20 x 20 / 12) x 1.15 = 33.3 x 1.15 = 38.3 FPM. This is the minimum conveyor speed at the sorter induction point to achieve 20 CPM with the largest carton. The tool carries the raw 33.33 through the whole sorter chain and rounds only the display, so every number below is built from full-precision inputs, not the rounded intermediates shown here.
The ratio of pitch to carton length. Tells you how much faster the sorter must run relative to the induction belt to maintain the gap that already exists.
Gap at induct = 33 in, Min L = 9 in. SGR = (9+33)/9 = 4.67. The gap fed to the sorter is the min carton's own Gap Produced (33 in), the binding induction gap from the section above, not the max carton's 44 in. The sorter must run 4.67x the induction belt speed for the min carton, which is why the min carton gap is the binding constraint, not the max carton. The tool carries every input at full precision and rounds only the final display.
The actual operating speed the sorter must run. Multiplies the minimum conveyor speed by the speed gap ratio. Use the MAX column as your design speed.
SGR (max carton) = 2.65, CFPM (max carton) = 38.3 FPM. Required Speed = SGR x CFPM = 101.6 FPM. The max carton governs here; round up to the next practical belt speed for the sorter run speed. Multiplying the rounded 2.65 and 38.3 by hand gives 101.5, but the tool chains the raw values at full precision and returns 101.6, rounding only at the end.
The actual gap between cartons at the confirmed sorter operating speed. This is the gap available for the sorter to physically divert each carton.
SorterSpeed=101.6 FPM, Rate=20 CPM, MaxL=20 in. Gap = (101.6 x 12 / 20) - 20 = 41.0 in. This 41 inch gap must be compared against both the model minimum gap and the geometric gap requirement. The tool carries the sorter speed at full precision rather than the rounded 101.6, so the chained result is 41.0 in.
The minimum physical gap the selected sorter model requires to complete a divert without the trailing carton entering the divert zone before the leading carton has cleared it. Driven by max carton width.
ProSort 121, MaxW=15 in. Model Min Gap = 9 in (per Hytrol spec: width 8-15 in requires 9 in minimum). The gap produced at sorter speed must equal or exceed this number.
The minimum gap the carton geometry requires for the widest carton to clear the divert without hitting the next carton. Two inches of safety margin is added.
MaxW=15 in, divert angle=30 degrees. Gap = (15 x SIN(30)) + 2 = (15 x 0.5) + 2 = 7.5 + 2 = 9.5 in. The gap produced must also meet or exceed this number.
The required belt speed of the takeaway spur conveyor. Because the carton exits the sorter at an angle, the spur must run faster than the sorter to maintain the carton's velocity component in the direction of travel.
SorterSpeed=101.6 FPM, divert angle=30 degrees. Spur Speed = 101.6 / COS(30) = 101.6 / 0.866 = 117.3 FPM. Round up to the next practical belt speed. This is the takeaway spur specification, not the sorter speed. The tool runs the spur off the required sorter speed at full precision, so it returns 117.3 FPM.
Transfer tab - rows 4 through 19
The 90 degree transfer calculations are covered in Lesson 25, The Gap Check and Capacity Proof. A transfer lifts a carton off the trunk line, moves it laterally to an adjacent conveyor, and lowers it. During this cycle the trunk line is still running. The calculation confirms whether the gap on the trunk line is large enough to complete the full cycle before the next carton arrives.
Every 90 degree transfer in a system is a potential collision point. The calculation tells you the minimum gap required. If the gap on the trunk line does not meet that minimum, you have a carton collision on every transfer cycle. I have seen this missed in proposals more than once. Run this calculation for every transfer in the system.
The distance the transfer mechanism must move the carton sideways. Assumes worst-case carton position on the side opposite the divert direction.
BF=21 in, OAW=24 in. Lateral Distance = 21 + ((24-21)/2) = 21 + 1.5 = 22.5 in. The transfer must move the carton 22.5 inches before the cycle is complete.
Total time the transfer mechanism is busy from the moment it lifts until it is back in the ready position. The trunk line cannot safely deliver the next carton during this window.
LiftTime=0.5 sec, LateralDist=22.5 in, TransferSpeed=30 FPM, LowerTime=0.5 sec. Cycle = 0.5 + (22.5/12)/(30/60) + 0.5 = 0.5 + 1.875/0.5 + 0.5 = 0.5 + 3.75 + 0.5 = 4.75 sec. The trunk line must have enough gap to keep the next carton away for 4.75 seconds.
The minimum gap needed between cartons on the trunk line for the transfer to complete a full cycle before the next carton arrives. Four inches of safety margin is added.
CycleTime=4.75 sec, TrunkSpeed=120 FPM. MinGap = (4.75 x 120 / 5) + 4 = 114 + 4 = 118 in. The gap between cartons on the trunk line must be at least 118 inches for this transfer to operate without collision.
Use this as a checklist when working through the calculator
Every calculation in the spec calc has dependencies. Running them out of sequence produces wrong answers that pass their checks but are wrong for the wrong reasons. Use this sequence every time.
| Step | Calculation | Feeds Into |
|---|---|---|
| 1 | Carton specs entered (L, W, H, WT) | All downstream calculations. This is the foundation. |
| 2 | Global conveyor inputs set (SpeedIn, SpeedOut, Gap, IR, BF, OAW) | Gap Produced, Curve BF, Theoretical Rate |
| 3 | Weight per Foot calculated | Roller capacity and incline belt checks (outside the calc) |
| 4 | Minimum Curve BF calculated | Curve conveyor specification in the proposal |
| 5 | Tumble Angle calculated | Maximum allowable incline angle. Sets a hard limit on layout. |
| 6 | Gap Produced calculated | Theoretical Rate, Pitch, Sorter induction gap input, Transfer gap check |
| 7 | Theoretical Rate confirmed | Confirms the system can achieve required CPM at set speed. If not, SpeedIn must increase. |
| 8 | Sorter: Required Rate entered | CFPM - must be confirmed with customer in writing before this step |
| 9 | Sorter: CFPM calculated | Required Sorter Speed via SGR |
| 10 | Sorter: SGR calculated | Required Sorter Speed |
| 11 | Sorter: Required Sorter Speed confirmed | Gap Produced at sorter, Takeaway Spur Speed |
| 12 | Sorter: Gap checks run (model min + geometry) | Go / No-go on sorter selection at this rate and product mix |
| 13 | Sorter: Takeaway Spur Speed calculated | Takeaway spur conveyor specification in the proposal |
| 14 | Transfer: Lateral Distance calculated | Transfer Cycle Time |
| 15 | Transfer: Cycle Time calculated | Minimum Gap Required on Trunk Line |
| 16 | Transfer: Gap check run | Go / No-go on trunk line speed and gap at this transfer point |
The most common mistake I see is running the sorter tab before confirming the required rate with the customer. CFPM is driven entirely by rate. If the rate changes after the calc is done, every sorter number is wrong. Get the rate in writing. Then run the calc.