Code of Maine Rules
18 - DEPARTMENT OF ADMINISTRATIVE AND FINANCIAL SERVICES
554 - BUREAU OF GENERAL SERVICES
Chapter 3 - LIFE CYCLE ANALYSIS
Section 554-3-III - Application

Current through 2024-38, September 18, 2024

III.A. Introduction

The Maine Life Cycle Energy Evaluation Technique

A.1. 0 Purpose: The procedures have been developed in response to actions taken by the Maine Legislature requiring the life cycle costing become a part of the evaluation process for public improvements to assure that energy considerations, first cost, operating costs and long term costs are consistently analyzed as public improvement projects are being considered for approval.

A.1. 1 Goals: It is readily recognized that the life long energy usage of a building is largely determined by the original design and selection of detail equipment. once a building has been erected, it becomes very expensive and difficult to modify construction to accommodate more energy conservation equipment.
(1) Energy Performance Index (EPI) Target goals have been established to limit total building energy usage.

(2) Analysis of Energy: The Maine Life Cycle Energy Evaluation Technique Program is intended to help the designer quickly evaluate his alternative designs to determine those which may save the most energy.

(3) Life Cycle Economic Analysis: An evaluation format to be used -in the. final design selection. This procedure identifies the initial capital cost and the owning cost (energy cost and equipment maintenance cost) to determine the life cycle costs throughout the project life.

A.1. 2 Summary: The purpose of the design standards is not to limit architectural freedom, but is intended to create an awareness that all designs must effectively minimize the use of energy.
(1) Hand Calculations: It is anticipated that the hand calculation method of analyzing the technical portion and the hand calculation method of financial analysis for life cycle costing will be adequate for most of the anticipated construction in the area of public education and state facilities.

(2) Computer Models: Computer programming for the analysis of both or either the technical or financial portions of the study will be acceptable to the Bureau if the Base Model meets the following requirements:
A. The Bureau has on file the operation manual of the program.

B. Base Model to be evaluated by B.P.I. or certified by a third party professional acceptable to B.P.I. and the applicant.

C. Submits unmodified base data runs of the analysis.

(3) Submissions: The following is the minimum requirements for submission of life cycle analysis to B.P.I.:
A. Building Energy Form "LCA-1"

B. Life Cycle Cost Form "LCA-2"

C. Solar Analysis (if applicable)

D. All backup calculations and data for all the above submitted energy and cost analysis.

E. Preparer's information to include name, affiliation, telephone number, registration (stamp or number), and date.

III.B. Energy Performance Index (EPI)

B.1. 0 Energy Performance Index (EPI)

B.1. 1 Introduction: The goal of this program is to encourage the development of the most energy conservative building that is consistent with current standards, codes and practices for the buildings intended use.

B.1. 2 Limits: In no instance will total building designed energy consumption exceed the following standards:
(1) Maximum Energy Goals: Goals are established from recent construction experience utilizing passive and active solar, energy recovery, alternate energy use and other innovated techniques.
A. Elementary and Junior High, Schools 40,000 BTU/s.f.

B. High Schools 45,000 BTU/s.f.

C. Vocational Technical Schools 50,000 BTU/s.f.

D. Office Buildings (12 month use)
i. New Construction 65,000 BTU/s.f.

ii. New Leased/Renovated 70,000 BTU/s.f.

E. Dormitories (9 month use)
i. Regular 45,000 BTU/s.f.

ii. Apartment Style 46,000 BTU/s.f.

(2) Base Energy Usage
A. Forty (40) hour week occupancy time. (The equipment-and lighting usage Shall reflect the hours required to maintain occupancy requirements for 40 hours. As a rule lighting and equipment hours are longer.)

B. The above listed BTU/s.f. limits are based on 100% system and equipment efficiency and shall be increased by an appropriate factor representing seasonal efficiency of the selected system and equipment to reflect estimated annual fuel use.

C. Values based on 8,000 degree days. Additional allowances will be allowed in locations where total degree days exceed 8,000 degree days according to the following table:

8,000 Degree Days 0
9,000 Degree Days 1,750 BTU/s.f.
10,000 Degree Days 3,500 BTU/s.f.
11,000 Degree Days 5,250 BTU/s.f.
12,000 Degree Days 7,000 BTU/s.f.

D. The Director, upon staff recommendations, may increase the above energy goals by 10% for historic buildings hardship occurrences, facility reuse and other non-reoccurring and unique circumstances.

FORM "LCA-1" B.2.0 Required Energy Items (Reporting Format)

Energy Conservation in Buildings

Building Name __________________________________________________

Building I.D. ___________________ Location _____________________________

(1) Average Number of Occupants ______.

(2) Degree Days ___________ /year

(3) Design Temperature ____________________.

(4) Building Area ___________________.

Energy/Point of Use Per Year

(5) Lighting ________________ Base _________ Units #1 __________ MBTU ___

(6) Heating ___________________ " _______________________ MBTU

(7) Cooling ___________________ " _______________________ MBTU

(8) Water Heating ___________________ " _______________________MBTU

(9) Equipment ___________________ " _______________________ MBTU

(10) Other ___________________ " ______________________ _MBTU

(11) Total Energy ___________________ " _______________________ MBTU

(12) Yearly Energy Usage ___________________ " _______________________ MBTU Per Building Square Foot Area

#1 Base Units of Energy - KWH of electricity, gallons of oil (#2, #4, #5 or #6), tons of coal, etc. shall be evaluated a N = 100% to determine annual energy consumption (BTU/square foot), Note: Apply factors on Page 8 Val and "N" to develop projected fuel usage (gallons of oil, tons of coal, etc.) to report on Form "LCA-2".

III.C. Analysis of Energy

C.1. 0 Approved Systems: The ASHRAE's Modified Degree Day Procedure will be used in analyzing the simple heating and ventilation systems. For those systems which involve computing cooling and night setback loads, internal and solar gains, the bin method or computer modeling is required.

Both methods are included in this document (see C.2.0 and C.4.0).

A sample is included in the Appendix A of the Modified Degree Day calculation.

C.2. 0 Modified Degree Day Procedure: (Chapter 43, ASHRAE 1980 System Handbook) The general equation for calculating the probable energy consumption by the modified degree day method is as follows:

E = (Hl x D x 24) (Cd)

(At x N x V)

where

E = Fuel or energy consumption for the estimate period.

Hl = Design heat loss, including infiltration, BTU per hour.

D = Number of 65° F degree days for the estimate period.

t = Design temperature difference, Fahrenheit.

N = Correction factor for equipment efficiency.

V = Heating value of fuel, consistent with H1 and E.

Cd = Interim correction factor for heating effect vs. degree days.

Values of heating load. Hl must be determined for the particular building for which the estimate is being made. It must account for size, building materials, architectural features, use, and climatic conditions. Table 1 gives values for Cd and N.

Table I

Correction Factor Vs. Degree Days Interim Factor Cd

Design Degree Days 6,000 7,000 8,000 9,000 l0,000
Factor Cd 60 .64.68 .71 .71

The correction factor N is empirical and should not be confused with any ratings for "seasonal efficiency" The following values shall be used:

N = 1 - Electric Resistance Heating

N = .75 - Pressurized Gas Fired Boiler or System

N = .70 - Oil Fired Boiler with Air Atomizing or Flame Retention

Burner

N = . 65 - Atmospheric Gas Fired System

N = .50 - Coal Fired Boiler Conventional Stoker

N = .65 - Coal Fired Boiler Pressurized Forced Draft Firing System

N = .55 - Old Oil Fired Systems

Note: If other values are to be used, submit verification and backup data.

C.2. 1 Table/Degree Data/Maine

Maine Monthly and Annual HEAting Degree Day Normals

Station July Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun annual
Bar Harbor 47 49 193 459 741 1153 1280 1137 998 669 381 133 7240
Caribou 84 122 327 657 1008 1516 1683 1459 1283 849 474 170 9632
East Port 117 109 246 499 762 1175 1314 1162 1048 744 499 258 7833
Farm- ington 40 75 239 555 891 1361 1500 1296 1107 705 364 104 8237
Gard- iner 29 51 204 502 816 1274 1414 1232 1060 681 364 99 7726
Green- ville 86 119 321 639 978 1460 1628 1417 1249 837 481 172 9387
Houl- ton 61 91 271 592 936 1426 1584 1369 1181 780 409 127 8827
Lewis- ton 12 33 163 456 798 1234 1383 1196 1035 657 331 76 7374
Madi- son 29 59 214 530 864 1339 1482 1285 1101 702 370 96 8071
Millin- ocket 38 65 245 580 912 1398 1553 1352 1147 741 398 104 8533
Old Town FAA 53 83 273 595 900 1380 1531 1347 1159 756 431 140 8648
Port- land 27 55 200 493 792 1218 1349 1179 1029 669 381 106 7498
Pres- que Is. 66 98 283 614 969 1473 1624 1408 1231 804 431 134 9135
Ripog- enus Dam 76 106 277 605 957 1466 1637 1450 1265 831 471 147 9288
Rock- land 41 57 195 481 765 1175 1293 1142 1008 672 397 127 7353
Rum- ford Pwr. Plant 36 64 216 521 858 1305 1438 1246 1076 693 361 98 7912
Water- ville Pump Station 20 32 181 477 810 1277 1417 1224 1039 642 319 75 7513
Wood- land 37 82 218 539 846 1305 1454 1294 1107 723 397 119 8121

C.3. 0 Hand Calculations Method for Life Cycle Analysis

DATE: ____________________ ARCHITECT ENGINEER:

__________________

LOCATION: ______________ DATA OBTAINED BY: ____

_____________

____________________

Energy needs for buildings can be divided into three basic categories: (1) Base Electrical Loads; (2) Comfort Conditioning System; (3) Domestic Hot Water. The calculation sequence has been segmented accordingly. The analysis must start with an understanding of the proposed building usage and will require detailed data on the sub-components of the electrical and HVAC system. This detailed data should be available as a result of (1) preliminary design and (2) analysis of methods that will optimize energy conservation within the building.

C.3. 1 Base Electrical Load: This section analyzes the annual electrical energy consumption due to the lighting systems HVAC system, (fans, pumps, etc.), exhaust fans, kitchens, shops, elevators, and other specialized operations. A "guideline" comment follows each topic area to clarify the type-of data sought. The diversity factor represents the fact that lighting, for instances is rarely all on or all off.
(1) Lights, Miscellaneous Power Usage:
A. KW connected ______________ KW

B. Usage _____ hrs./day x ___ days/week ______ hours/month 12 month/year = ___________ hours/year

C. Diversity __________ %

D. ________ KW x ________ Diversity = _________ KW

E. ________ KW x ________ hours/year = _________ KWH/year

Guidelines:

i. Example: 8 hours/day + 4 hours for lunch and cleanup = 12 hours/day.

ii. Weeks/Month - 4.3

iii. 80 - 100% Diversity

(2) Air Distribution System Electrical Usage (Heating, Cooling and Ventilation):
A. HP connected ________ HP

B. 746 KW/HP x _____ HP = ______

C. Diversity _________ %

D. Occupied __________ hours/month

E. Unoccupied _________ hours/month

F. _________ KW x ____________ Diversity = __________ KW

G. _________ KW x ______ hours/month = _________ KWH/month

H. _________ KWH/month X ________ month/year = _______ KW/year

Guidelines:

i. Hours Operation: 400 hours/month or 4000 to 4800 hours/annum.

ii. 80% Diversity

iii. Will system operate during unoccupied hours"

(3) Exhaust Fan System Usage:
A. HP connected __________ HP

B. .746 KW/HP x __________ HP = __________ KW

Efficiency _________

C. Occupied .__________. hours/month

D. Diversity _______ %

E. Usage: 25% x Occupied Hours _______ hours/month

F. _________ KW x _______ Diversity ________ KW

G. _________ KW x _____ hours/month ______ KW/month

H. _________ KWH/month x ------- month/year ______ KWH/year

Guidelines:

i. Hours Operation: 300 hours/month 3600 to 4000

ii. 100% Diversity

iii. Will system operate during unoccupied hours"

(4) Elevator Usage (if required)
A. HP connected ___________

B. .746 KW/HP x ._________. HP = _______ KW

Efficiency ___________

C. Occupied ._______. hours/month

D. Diversity _______ %

E. Usage: 25% x occupied hours = ________ hours/month

F. _______ KW x _______ Diversity = KW

G. _______ KW x ________ hours/month = ___________ KW/month

H. _______ KWH/month x_______ month/year ________ KWH/year

Guidelines:

i. 50% Diversity for office Buildings

ii. 25% Usage for Office Buildings

C.3. 2 Comfort Conditioning System: Similar to the previous section, this section emphasizes the derivation of the annual energy consumption for the HVAC system for space beating and cooling. But since heating and cooling is functionally related to ambient environment, a different technique must be utilized to derive annual energy temperature differential between inside and ambient a separate calculation using "bin" method is necessary. The method statistically arranges weather data in "bins" by day period according to 5° F increments and numbers of hours per year.
(1) Building Load Information
A. Winter Heating - Outside Design _______ F°D.B.

Inside Design ______ F°D.B.

Heat Loss ______ BTUH

Ventilation

__________ CFM x 1.08 x _________ °FTD = _______ BTUH

Total Heat Loss _______ BTUH

B. Summer Cooling - Outside Design _______ °F.D.B. ________ °F.W.B.

Inside Design __________ °F.D.B.

Solar Heat Gain __________ BTUH

Transmission ______________ BTUH

Motors _____________________ BTUH

Lights ________________________ BTUH

People _________________________ BTUH

Other Heat Sources _________________ BTUH

Ventilation ___________________________ BTUH

CFM x 4.5 x ______ Ah** ______ BTUH

Total Heat Gain ________ BTUH

*Notes: This load information should include both sensible and latent heat requirements.

**AH - Enthalpy at Saturation BTU Per Pound of Dry Air

C.4. 0 Bin Method: See Chapter 43, ASHRAE 1981 Systems Handbook for General Reference

C.4. 1 Explanation of Forms

C-1 Heating Form (see Appendix C)

C-2 Cooling Form (see Appendix C)

Column 1 Three eight hour periods during the day.

Column 2 Average monthly temperature from weather data.

Column 3 Temperature difference equals temperature inside minus (AVG) temperature outside.

Column 4 "U" value times area equals heat gain or heat loss per degree of temperature, including infiltration & ventilation or greater of the two.

Column 5 Column 3 times Column 4

Column 6 Hours listed in the weather data of each "bin' of temperature.

Column 7 Column 5 times Column 6

Column 8/8a Peak internal load in MBTU: Peak solar load in MBTU.

Column 9/9a Annual Factor in a percentage of the time that the internal available internal & solar gain must be rejected during day occupied cycle.) or solar loads occur, and are useable. (Note: A percentage of the

Column 10 Estimated hours of internal load.

Column 10a Same as Column 6. (For C-2 Cooling Form Only)

Column 11 Column 8 x 9 x 10.

Column 11a Column A x 9a (For C-1 Heating Form Only)

Column 12 Column 7 + 11 + 11a.

C.4. 2 Passive Solar

Values for t in solar analysis shall be determined using the three eight hour periods above.

C.4. 3 Heating Energy
(1) Electric Consumption

A.________ MBTU/YR. = _________ MBTU/KWH = ________ KWH/YR.

Guidelines:

(1) Resistance Heating 3.413 MBTU/KWH

(2) Oil Consumption

A.______ MBTU/YR. x MBTU/GAL. = _________ GAL/YR.

Boiler Efficiency

Guidelines:

i. #2 oil = 140 MBTU/GAL.

(3) Energy Performance Index (Annual)
A. Electrical Heating Consumption.
i. ______ KW/HR: _________ Gross Sq. Ft. = ________ KWH/SQ.FT.

ii. ____________ KWH/SQ. FT. x 3.413 MBTU/KWH __________ MBTU/SQ. FT.

B. Heating Consumption (Oil Fired)
i. _________ GAL.: x ________ Gross Sq. Ft. GAL/SQ. FT.

ii. _________ KWH/SQ. FT. x ________ MBTU/GAL. = ________ MBTU/SQ. FT.

C.4. 4 COOLING ENERGY
(1) Electrical Consumption
A. ______ MBTU/YR : 12 MBTU/TON = _________ TON HR/YR.

B. ______ TON/HR/YR x ______ KW/TON = _______ KWH/YR.

Guidelines:

i. Reciprocating Equipment 1.2 to 1.7 KW/TON

ii. Centrifugal Equipment .75 to 1.1 KW/TON

(2) Absorption System Consumption (Oil Fired)
A. MBTU/YR. : 12 MBTU/TON TON/HR/YR.

B. TON/HR/YR. x GAL/TON = GAL/YR.

Guidelines:

i. High Pressure Absorption .1 GAL/TON

ii. Low Pressure Absorption .13 GAL/TON

(3) Energy Performance Index (Annual)
A. Electric Cooling Consumption
I. ________ KWH : ________ Gross Sq./Ft. = _______ KWH/Sq./Ft.

ii. _______ KWH/SQ.FT. x 3,413 MBTU/KWH = ______ MBTU/Sq./Ft.

B. Absorption System Consumption (Oil Fired)*
i. ______ GAL x 140 MBTU = ________ MBTU/HR.

ii. __________ MBTU: _________ Gross Sq. Ft. = _________ MBTU/Sq./Ft.

*Absorption system run by 'waste' heat or by solar heat should not be included.

C. Annual Cost for Each System: Electric cost can be calculated on a demand commodity. Rate schedule or an average cost per KWH.

Guidelines:

i. Electrical Cost

________ KWH/YR. x ________ cents/KWH = $ _______ YR.

ii. Fossil Fuel Cost
a. Fuel Oil Cost

_______ GALS/YR x _____ cents/GALS = ______ $ YR

b. Coal

_________ TON COAL/YR. x ________ $/TON = $ ________ YR.

c. Steam

________ POUNDS OF STEAM/YR. x ______ cents/POUND = $ ________ YR.

C.5. 0 Computer Method for Energy Analysis
(1) Computer programs that provide a simulated analysis of a facility for a complete year of usage will be considered by B.P.I. The computer base model will be evaluated by B.P.I. or certified by a third party professional acceptable to B.P.I. and the applicant. The following data must be submitted and kept on file at B.P.I.:
A. Program Operation Manual.

B. A dump of the basic computer program or submission of base data used in the program.

C. A computer run (unmodified) of a base data building. Base data building to be selected by B.P.I.

(2) Computer Programs Now Acceptable
A. "ECM 5" currently running on the University of Maine at Orono main computer.

B. "BPI Model" currently being run on the Bureau of General Services in-house computer "TRS 80".

C.6. 0 Passive Solar

This section analyzes the energy gains and losses due to southern exposed glass. The windows analyzed under this section should not be included in the previous sections, but shall be added on to obtain the total energy usage in the building.

(1) EQ (1) Qtotal Qgain - Qcond

Where:

Qtotal = net energy, if positive then it represents a gain in energy and shall be subtracted from the building energy load; if negative then it represents a loss of energy and shall be added to the energy load.

(2) EQ (2) Qgain = (B) (C) (ST) (A) (D)

Where:

Qgain = solar gain through southern exposed glass.

B = Btu/sq. ft. day, see solar intensity table.

C = Percentage of possible sunshine, see table.

ST = Percentage of solar transmittance, obtained from window manufacturer.

A.= Area of glass.

D = Days in month analyzed.

(3) EQ (3) Qcond = (U1 [DELTA]t1 + U2 [DELTA]t 2 + U2 [DELTA]t3 ) (8) (D) (A)

Where:

Qcond = Energy conducted through the glass.

U 1 = U factor during the day.

U 2 = U factor during the night (if different from U).

KW Efficiency ------ %

[DELTA]t 1 = Inside temperature minus average outdoor temperature during the day.

[DELTA]t 2 = Inside temperature minus average outdoor temperature during early morning period.

[DELTA]t 3 = Inside temperature minus average outdoor temperature during the night.

D = Days in month analyzed.

A = Area of glass.

Values of [DELTA]t are determined using the BM method (see Section C.4.2.)

SOLAR INTENSITY TABLE

PORTLAND

Month *BTU/square foot day **% of Sunshine
January 860 55
February 1,044 59
March 1,113 56
April 1,051 56
May 947 56
June 904 60
July 924 64
August 1,092 65
September 1,153 61
October 1,138 58
November 825 47
December 735 53

* Obtained from Passive Solar Design Handbook. Volume 2.

** Obtained from Local Climatological Data for Portland, Maine.

Example Problem: For a southern exposed double glazed window, for the month of January.

January [DELTA]t1 = (68-27) = 41

[DELTA]t2 = (68-18.7) = 49.3

[DELTA]t3 = (68-21.4) = 46.6

B = 860, C = .55, ST = .73

A = 20

U1 = .53

U2 = With panel of R-7 placed over the windows at night - U2 = .14.

EQ (2) Qgain = (B) (C) (ST) (A) (D)

= (860) (.55) (.73) (20) (31) = 214,080 BTU/month

With Insulated Panel:

EQ (3) Qcond = U1 [DELTA]t1 + U2 [DELTA]t2 + U2 [DELTA]t3) (8) (D) (A)

= (.53 x 41 + .14 x 49.3 + .14x46.6) (8) (31) (20)

174,374 BTU/month

EQ (1) Qtotal = Qgain - Qcond

= 214,080 - 174,374 = 39,706 BTU/month gain.

This value is to be subtracted from the buildings total energy usage.

Without Insulated Panel:

EQ (2) Qgain = 214,080

EQ (3) Qcond = (41 + 49.3 + 46.6) (.53) (8) (31) (20)

= 359,883 BTU/month

EQ (1) Qtotal = Qgain = Qcond

= 214,080 - 359,883 = -145,803 BTU/month loss.

This value is to be added to the buildings total energy usage.

C.7. 0 Active Solar Analyzing

All active solar systems shall be analyzed separate from this rule and submitted to the Bureau of General Services for review. The designer must compare alternate combinations of heating systems and document. An acceptable Life Cycle Analysis shall include, but not be limited to, the following scope: 10% cost of money, total system cost, system efficiency, total estimated available energy/sq. ft. of panel, total estimated useable energy, component life, and operational and maintenance cost.

Exclusions to this rule are as follows:

(1) Financing of the total system is from other than State funds.

(2) The system is for education purposes and accepted in writing by DECS, Dept. of Educational and Cultural Services. (Single panel for science lab etc.)

Building energy credits would be applicable at such time the actual cost of the system is known.

III.D. Life Cycle Costing/Financial Analysis

D.1. 0 Introduction

Life Cycle Costing is a conceptual extension of the conventional method for awarding contracts to the lowest bidder. Instead of focusing just on the initial costs Life Cycle Costing takes into account the additional costs for energy, operation and maintenance , and system replacements. In this manner, all costs associated with building ownership are fully taken into account when selecting the best alternative design. The overall objective of Life Cycle Costing is more extensive than conventional first cost analysis since it seeks to evaluate the quality of the building over it s lifetime. This concept is especially important when energy costs are rapidly increasing.

D.2. 0 Hand Calculation

The Life Cycle cost evaluation has been established utilizing the uniform annual cost model.

The annual cost model has been developed by forecasting all cost, whether positive or negative, involved with the total system over its projected life. These costs are divided into annual payments taking into account the time value of money for an appropriate interest rate associated with the project.

For the purpose of our project, a 10% rate has been assigned. We have also assigned a 30 year life to the building structure.

Mathematically we are using a uniform recover rate as follows:

Click here to view Image

A = uniform end of year sum

P = present value of today's cost.

i = interest rate for period.

y = number of years.

Table has been included with values for given interest and applicable years,

*Material from text by K and G Associates, Box 7596, Inwood Station, Dallas, Texas 75209.

State of Maine FORM "LCA-2,"

DATE _________

D.3. 0 Life Cycle Cost Benefit Analysis PREPARED BY _________ (Reporting Format)

PROJECT ________ DISCOUNT RATE _________

Column Identification A B C D E F G
Item Estimated First Cost P Est. Life UCR (P-A) Factor salvage (1st cost salvage UCR=A salvage x interest remarks
Site Development
Building Structure (All items exclusive of those listed below
Roofing
Conveying Systems
Mechanical
Electrical
Equipment Built-In
Total Estimated Construction Cost Sub Totals COL. E
Energy Usage Annual Cost COL. F carriage return
amt. type
Heating Fuel (oil, gas, coal, elec.
Electricity (except heat)
Sewer
Insurance
Taxes (Or Loss)
Maint. & Repair
Maint. Contracts
Other
Total Uniform Annual Sum
Uniform Annual Sum/Sq. Ft. AIA GROSS SQ. FT _______

D.4. 0 Interest Table

10% Interest Factors

Year SCA SPW UCA USF UCR UPW
Y P-F F-P A-F F-A P-A A-P
1 1.100 .9091 1,000 1.000 1.000 0.909
2 1.210 .8264 2,100 .4762 .5762 1.736
3 1.331 .7513 3,310 . 3021 .4021 2.487
4 1.464 .6830 4,641 . 2155 .3155 3.170
5 1.611 06209 6,105 .1638 .2638 3.791
6 1.772 .5645 7,716 .1296 .2296 4.355
7 1.949 .5132 9,487 .1054 .2054 4.868
8 2.144 .4665 11.44 .0874 .1874 5.335
9 2.358 .4241 13.58 .0736 .1736 5.759
10 2.594 .3855 15.94 .0628 .1628 6.144
11 2.853 .3505 18.53 .0540 .1540 6.500
12 5.054 .1978 40.54 .0247 .1247 8.022
15 5.560 . 1799 45.60 .0219 .1219 8.201
19 6.116 .1635 51.16 .0196 .1196 8.365
20 6.727 .1486 57.28 .0175 .1175 8.514
21 7.400 .1351 64.00 .0156 .1156 8.649
22 8.140 .1228 71.40 .0140 .1140 8.772
23 8.954 .1117 79.54 .0126 .1126 8.883
24 9.850 .1015 88.50 .0113 .1113 8.985
25 10.84 .0923 98.35 .0102 .1102 9.077
30 17.50 .0573 164.5 .0061 .1061 9.427
35 28.10 .0356 271.0 .0037 .1037 9.644
40 45.26 .0221 442.6 .0023 .1023 9.779
45 72.89 .0137 718.9 .0014 .1014 9.863
50 117.4 .0085 1164. .0009 .1009 9.915
60 304.5 .0033 3035. .0003 .1003 9.967
70 789.7 .0013 7887. .0001 .1001 9.987
50 2048. .0005 20474. .0001 .1001 995
90 5313. .0002 53120. .0000 .1000 9.999

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