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    • HERS RATER WRITTEN EXAM >
      • Section 1 Building Science Fundamentals >
        • 1a. Basic Terms & Definitions >
          • 1. Airflow in Buildings
          • 2. Equipment Efficiencies
          • 3. Power and Energy
          • 4. Effective Leakage Area
          • 5. Area Weighted R-Value
          • 6. Baseload / Seasonal Energy Use
          • 7. Driving Forces (Including Natural and Mechanical)
          • 8. Behavior of Radiation
          • 9. Thermal Resistance / Transmittance: R and U Values
          • 10. Latent / Sensible Heat
          • 11. Total Equivalent Length
          • 12. Dehumidification / Humidification
          • 13. Convert Pressure Units
          • 14. Thermal Bridges
          • 15. Pressure Boundary
          • 16. Stack Effect
          • 17. Exfiltration and Infiltration
          • 18. Natural / Mechanical Ventilation
          • 19. Net Free Area
          • 20. Input & Output Capacity
          • 21. Peak Electrical Demand
          • 22. Permeability and Perm Rating
          • 23. Standby Loss
          • 24. IAQ (indoor air quality): Moisture, CO, Dust
        • 1b. Principals of Energy, Air & Moisture Thermodynamics >
          • 1. Thermodynamics: Conduction, Convection, Radiation, ΔT
          • 2. Factors That Affect Insulation Performance
          • 3. House Pressurization/Depressurization by Various Forces
          • 4. Heat Gain / Loss
          • 5. Power and Energy
          • 6. Moisture Transport Mechanisms
          • 7. Identify Areas of Highest Relative Humidity
          • 8. Principles of Combustion
        • 1c. Combustion Safety >
          • 1. Combustion Analysis
          • 2. Carbon Monoxide (CO) Testing
          • 3. Combustion Appliance Venting, Draft, Combustion Air & Sizing
          • 4. Understand Combustion Safety Issues
      • Section 2 Buildings and Their Systems >
        • 2a. Building Components >
          • 1. Identify basic duct configurations and components
          • 2. Identify Basic Hydronic Distribution Configurations and Components
          • 3. Identify Basic Structural Components of Residential Construction
          • 4. Thermal Boundaries and Insulation Applications
          • 5. Basic Electrical Components and Safety Considerations
          • 6. Basic Fuel Delivery Systems and Safety Considerations
          • 7. Basic bulk water management components (drainage plumbing gutters sumps etc)
          • 8. Vapor barriers/retarders
          • 9. Radiant Barrier Principles and Installations
          • 10. Understand Fenestration Types and Efficiencies
          • 11. Understand Issues Involved With Basements, Crawlspaces, Slabs, Attics, Attached Garages, Interstitial Cavities, and Bypasses
          • 12. Understand Issues Involved With Ventilation Equipment
          • Understand Basic Heating / Cooling Equipment Components Controls and Operation
          • Understand Basic DHW Equipment Components Controls and Operation
          • Identify Common Mechanical Safety Controls
          • Identify Insulation Types and R-Values
          • Understand Various Mechanical Ventilation Equipment and Strategies: Spot, ERV, HRV
        • Conservation Strategies >
          • Appropriate Insulation Applications and Installation Based On Existing Conditions
          • Opportunity for ENERGY STAR Lighting and Appliances
          • Identify Duct Sealing Opportunities and Applications
          • Understand Importance of Air Leakage Control and Remediation Procedures
          • Blower Door-Guided Air Sealing Techniques
          • Water Conservation Devices and Strategies
          • Domestic Hot Water (DHW) Conservation Strategies
          • Heating & Cooling Efficiency Applications
          • Proper Use of Modeling to Determine Heating and Cooling Equipment Sizing and Appropriate Energy
          • Understand the Use of Utility History Analysis in Conservation Strategies
          • Appropriate Applications For Sealed Crawlspaces Basements and Attics
          • Identify / Understand High Density Cellulose
          • Appropriate Applications for Fenestration Upgrades Including Modification or Replacement
        • Comprehensive Building Assessment Process >
          • Determine Areas of Customer Complaints / Concerns in Interview
          • Understand / Recognize Need For Conducting Appropriate Diagnostic Procedures
          • Interaction Between Mechanical Systems, Envelope Systems and Occupant Behavior
        • Design Considerations >
          • Appropriate Insulation Applications Based On Existing Conditions
          • Understand Fire Codes as Necessary to Apply Home Performance in a Code-Approved Manner
          • Understand / Recognize Building Locations Where Opportunities for Retrofit Materials
          • Understand Climate Specific Concerns
          • Understand Indoor Environment Considerations for the Environmentally Sensitive
          • Understand Impact of Building Orientation, Landscape Drainage, and Grading
          • Opportunity Potential Renewable Energy Applications: Geothermal, Photovoltaic, Wind
          • Understand Impact of Shading on Heating / Cooling Loads
          • Awareness for Solar Gain Reduction / Solar Gain Opportunities
          • Understand Need for Modeling Various Options For Efficiency Upgrades
      • Measurement & Verification of Building Performance >
        • Measurement & Verification of Building Performance >
          • Air Leakage Test Results
          • Understand Building Shell / Envelope Leakage
          • Apply Fundamental Construction Mathematics and Unit Conversions
          • Calculate Building Tightness Levels (Minimum Ventilation Requirements)
          • Calculate Heating Degree Days and Cooling Degree Days
          • Identify Proper Appliance and Combustion Appliance Venting
          • Ventilation calculations and strategies
          • Proper methods for identifying / testing fuel leaks
          • Blower door setup, accurate measurement and interpretation of results
          • Combustion Appliance Zone (CAZ): depressurization, spillage, draft, Carbon Monoxide (ambient and flue)
          • Carbon Monoxide (CO) evaluation: ambient
          • Proper applications and use of temperature measuring devices
          • Pressure pan and room to room pressure diagnostics
          • Recognize contributing factors to comfort problems
          • Inspect for areas containing moisture or bulk water in undesirable locations
          • Understand and inspect for basic electric safety (e.g. frayed wires, open boxes, etc)
      • RESNET HERS RATER National Standards & Project Specifications >
        • Understand applicability content and intent of BPI National Standards – Do no harm, make buildings more healthy, comfortable, durable and energy efficient
        • Recognize need for a professional local/state/national codes evaluation
        • Be able to specify appropriate materials and processes needed for building performance projects
      • Analyzing Buildings Systems >
        • Recognize need for air sealing measures and their impact on other building systems
      • Conduct and Communications >
        • Conservation strategies
        • Conservation strategies
    • HERS RATER FIELD EXAM >
      • How To Put The House Under Worst Case & CAZ
      • What's What? Pa, CFM, CFM50, CAZ, Draft, Room Pressure
      • What To Know In The Attic
      • What To Know In The House
    • BLOWER DOOR TEST >
      • Manometer Setup
    • RESNET STANDARDS >
      • RESNET Standards Decoded
  • ESSENTIALS
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    • COMMON AUDITOR / CREW MISTAKES
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HERS Rater Math Problems For People That Hate Math

FREE HERS RATER PRACTICE EXAM

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You are not alone, math is typically the most disliked topic on the HERS Rater Exam.  It can be confusing when to use the right equation or the difference between the ACH and MRV equations.  This section will help walk you through the math equations on the HERS Rater exam. 

You will see 11 different types of equations and math problems on the HERS Rater exam.  None of them are more than 4 steps so don't get overwhelmed.  With practice and repetition these math questions become easier and easier to do.

1. Conversions - kWh, watts, therms, & BTU's

Common questions on the HERS Rater exam and HERS Rater practice exams ask you to convert between units of power and energy (multiply power by time) or between kWh, therms and BTU's.  Some important conversions that you will just have to remember are:
100,000 BTU = 1 therms 
1,034 BTU     = 1 CCF

3412 kWh      = 1 BTU
3.412 Wh       = 1 BTU
1,000 watts   = 1 kW

12,000 BTU    = 1 ton
- given BTU's  and you need to find therms
- given BTU's to find cubic feet of gas
- given kWh and you need to find BTU's
- given watt-hrs and you need to find BTU's
- given watts and you need to find kW
- given BTU's and you need to find tonnage
If you are given BTU and need to find kWh, therms or CCF (or any other energy unit)...
DIVIDE BTU'S BY YOUR MAGIC CONVERSION NUMBER

If you are given kWh, therms or CCF and need to convert to BTU's...
MULTIPLY kWh, THERMS ETC BY YOUR MAGIC CONVERSION NUMBER
A BTU is the universal language of energy.  It doesn't matter if you have gas or electric appliances, therms, CCF or kWh in your bill, it all can be converted to BTUs to find and compare things like:

  1. How much an appliance costs to operate over a period of time
  2. How much energy is consumed over a period of time
  3. If it is cost effective to switch from an electric to a gas appliance

You can also use the conversion table below to switch between units of energy (power is a different table).  To use the table, start with what unit you are given and find it and go down in the "Existing Unit" column.  Then go across horizontally to the "Desired Unit" to the right and find the unit you need to convert it to.  The number you reach is your magic conversion number you can use by just multiplying your given "Existing Unit" number by the magic conversion number just found to get units of your "Desired Unit."

Here is a BPI sample question on conversions.

1. Find the amount of energy used in BTU's of a 60 watt light bulb which is on for 2 hours.
Answer: 
Given 60 watts (units of power, we want energy) and its running for 2 hrs.  
We will use the formula:
Energy = Power x time
Energy = 60 watts x 2 hrs
Energy = 120 watt-hrs

Now let convert watt-hrs to BTUs.  If you first try to convert watts to BTU using the table, you will find there is no unit for just watts in the table!  That should tell you that you need to convert it first.  Now we can find watt-hrs our table and go across until you hit the BTU column.  What is the magic conversion number?  It is 3.412.  So we just multiply our given energy use (120 watt-hrs) by the magic conversion factor for the answer.
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120 watt-hrs x 3.412 = 409.44 BTU

Now to get comfortable with this, let's find how many watt-hrs is in 409.44 BTU using our table.

409.44 BTU x (magic conversion number) = watt-hrs
409.44 BTU x 0.293 = 119.966 or rounding up we get 120 watt-hrs, the same answer we started with!

2. Cost and Energy Use

Cost Calculations

Finding the cost to operate a furnace or appliance should always be last, after you have found the energy use.  You will be given to utility rate ($0.11 a kWh or $1.20 per therm) and you have to find the energy use.

Energy Use Calculations

You will be given the power use (BTU/hr or kW) and a time the appliance is running, (5 hrs for 10 days).  You just need to multiple the one by the other.  You may have to do some conversions here to therms, kWh or CCF to BTUs (our universal language).  See the section above about multiplying or dividing by our magic conversion number.

Here is a BPI sample question on cost and energy use.

2. Find the electrical use of a furnace using 800 watts of power running 5 hours a day for 12 days.
Answer: 
Given: 
time running = 5 hrs per day x 12 days = 60 hrs per day
energy use = power x time 
                 = 800 watts x time
                 = 800 watts x 60 hrs per day
                 = 48,000 watts per hr per day or 48,000 watt-hrs

3. Using information from problem 2 above, how much does it cost to run the furnace if the electrical rate is $0.20 per kWh?
Answer:
energy use = 48,000 watt-hrs, we need to convert watts to kWh by multiplying by 0.001 or dividing by 1000, whatever you prefer.

watt-hrs converted to kWh
48,000 watt-hrs x 0.001 kWh/watt-hrs = 48 kWh
or 48,000 watt-hrs / 1,000 watt-hrs/kWh = 48 kWh

48 kWh x utility rate = cost
48 kWh x $0.20 per kWh = $9.6 per kWh

3. Payback and SIR

Payback = cost / savings

SIR = savings x life / cost
Any SIR greater than 1 is good

A good rule of thumb to ask yourself, "does this make sense?"  If your appliance cost $2,000 and your annual savings is only $300, does it make sense that your payback is less than a year (0.15 if you took the formula flipped)?  If not, try flipping your equations around and don't pick the answer on the exam too fast.

4. Windows and Area

length x width = area

If you are given a wall, door and window find the total area of the wall, then subtract the area of the window and door out of the total to find the net wall area.

Find a missing side or roof length given the base and height - use Pythagorean Theorem
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Let's do a sample problem you might see on the BPI exam with area and the Pythagorean theorem.
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Let's tackle this by breaking up the garage floor plan into two parts and finding the area for each section

Garage 1: 20’ x 5’  =  100 sq ft

Garage 2: treat the triangle as a 5’ x 5’ box; area of box is 25 sq ft; 25 sq ft / 2  =  12.5 sq ft

Garage 1 + Garage 2 = total sq ft
    100     +     12.5    = 112.5 sq ft

Now, let's find the perimeter of the garage floor plan above.

Garage 2 option 2: use the Pythagorean theorem to find the length of the missing side and then add the outer lengths together.
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5. R-value and U-value

1/R = U-value

1/U = R-value



U-values are for the total composite of an object such as a window (sash, frame, air space, glass, low-e coating) or entire wall (including frame, felt paper, insulation, drywall). U-values can not be added, but can be multiplied. 

R-values are for just one component and can be added together.

Given the U-value, you find the R-value by by taking 1 over the U-value.

Given the R-value, you can find the U-value by taking 1 over the R-value.

6. HDD and CDD - Heating Degree Day and Cooling Degree Day

Balance point of HDD = 65 degrees


Balance point of CDD = 78 degrees
The HDD is a tool for predicting heating costs.

Example: Today's temperature was 10 degrees as a low and 40 degrees as a high. What is the HDD?

  1. Take the average of the high and the low temperatures - (10 + 40) / 2 = 25
  2. Subtract your average temperature from the balance point - 65 - 25 = 40
  3. HDD = 40

7. MVR - Minimum Ventilation Requirement

MVR = 0.35 x Volume / 60

8. ACH

CFM50 x 60 / Volume

9. Baseline and Seasonal Useage

  1. Find the total useage from a 12 month usage table - write that number down
  2. Circle the 3 lowest months from a 12 month utility usage table
  3. Find the average of the 3 lowest months (Month 1 + Month 2 + Month 3)/3
  4. Multiply the average of the 3 lowest months by 12 = BASELOAD
  5. Subtract #1 by #4 (aka subtract the total useage - BASELOAD) = SEASONAL USEAGE

10. Draft 

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