# P&K KFA (VDI 3781 part 4)

## Sample Report (Log)

# Sample A 1 from the guideline. Real building ensemble

## Calculation for the exhaust gas discharge system 'X1'

### Details for Outlet building 'House 3' - Symmetric pitch roof α ≥ 20°

Quantity | Parameter | Value |
---|---|---|

Height of ground over origin of coordinates (Section 6.2.4, Figure 10) | Δh | 0.00 m |

Ridge height | H_{First} | 10.40 m |

Eaves height (Figure 4) | H_{Traufe} | 6.70 m |

Actual roof height (Figure 4, Section 6.2.1.2.2) | H_{Dach} | 3.70 m |

Width of half of the gable end opposite the outlet. For symmetric roof this will be b/2 else b | b_{Luv} | 5.65 m |

Horizontal distance between the center of the outlet cross-section and the ridge (Figure 4) | a | 0.00 m |

Roof pitch angle (Figure 4) | α | 33.22 ° |

Roof pitch correction (interpolated with table 2) | γ | 2.15 ° |

Factor for determining H_{2} (interpolated with table 2) | f | 0.66 |

Height of recirculation zone for distance a to ridge (Equation 1) | H_{1} | 0.00 m |

Maximum height of the recirculation zone (Equation 2) | H_{2} | 2.43 m |

Calculated height of exhaust gas discharge system over ridge (Equation 3) | H_{S1} | 0.00 m |

### Details for building 'House 1' - Symmetric pitch roof α ≥ 20°

Quantity | Parameter | Value |
---|---|---|

Height of ground over origin of coordinates (Section 6.2.4, Figure 10) | Δh | -2.10 m |

Ridge height | H_{First} | 11.50 m |

Eaves height (Figure 4) | H_{Traufe} | 7.50 m |

Actual roof height (Figure 4, Section 6.2.1.2.2) | H_{Dach} | 4.00 m |

Width of half of the gable end opposite the outlet. For symmetric roof this will be b/2 else b | b_{Luv} | 6.70 m |

Horizontal distance between the center of the outlet cross-section and the ridge (Figure 4) | a | 0.06 m |

Roof pitch angle (Figure 4) | α | 30.84 ° |

Roof pitch correction (interpolated with table 2) | γ | 0.56 ° |

Factor for determining H_{2} (interpolated with table 2) | f | 0.69 |

Height of recirculation zone for distance a to ridge (Equation 1) | H_{1} | 0.04 m |

Maximum height of the recirculation zone (Equation 2) | H_{2} | 2.76 m |

Calculated height of exhaust gas discharge system over ridge (Equation 3) | H_{S1} | 0.04 m |

Horizontal extend of the recirculation zone (Equation 15, Figure 8) | l_{RZ} | 18.20 m |

Effective length of an upstream building (Equation 16, Figure 8) | l_{eff} | 13.44 m |

Angle between the gable side of the upstream building and the line to exhaust gas discharge system (Section 6.2.2.1, Figure 8) | β | 89.87 ° |

Horizontal distance of the exhaust gas discharge system from the upstream building (Figure 8) | l_{A} | 17.52 m |

Height of the outlet required by the upstream buildings over the ridge of 'House 3' (Equation 17, Figure 8) | H_{S2} | -8.64 m |

### Details for building 'House 5' - Symmetric pitch roof α ≥ 20°

Quantity | Parameter | Value |
---|---|---|

Height of ground over origin of coordinates (Section 6.2.4, Figure 10) | Δh | 1.70 m |

Ridge height | H_{First} | 11.00 m |

Eaves height (Figure 4) | H_{Traufe} | 6.10 m |

Actual roof height (Figure 4, Section 6.2.1.2.2) | H_{Dach} | 4.90 m |

Width of half of the gable end opposite the outlet. For symmetric roof this will be b/2 else b | b_{Luv} | 7.80 m |

Horizontal distance between the center of the outlet cross-section and the ridge (Figure 4) | a | 6.22 m |

Roof pitch angle (Figure 4) | α | 32.14 ° |

Roof pitch correction (interpolated with table 2) | γ | 1.42 ° |

Factor for determining H_{2} (interpolated with table 2) | f | 0.67 |

Height of recirculation zone for distance a to ridge (Equation 1) | H_{1} | 3.69 m |

Maximum height of the recirculation zone (Equation 2) | H_{2} | 3.29 m |

Calculated height of exhaust gas discharge system over ridge (Equation 3) | H_{S1} | 3.29 m |

Horizontal extend of the recirculation zone (Equation 15, Figure 8) | l_{RZ} | 23.68 m |

Effective length of an upstream building (Equation 16, Figure 8) | l_{eff} | 19.54 m |

Angle between the gable side of the upstream building and the line to exhaust gas discharge system (Section 6.2.2.1, Figure 8) | β | 76.37 ° |

Horizontal distance of the exhaust gas discharge system from the upstream building (Figure 8) | l_{A} | 16.83 m |

Height of the outlet required by the upstream buildings over the ridge of 'House 3' (Equation 17, Figure 8) | H_{S2} | 1.35 m |

### Height of recirculation zones for the upstream buildings

at the outlet system 'X1' over ridge 'House 3'

Name of the building | Height of recirculation zone H_{S2} |
---|---|

House 1 | -8.64 m |

House 5 | 1.35 m |

### Calculation for the outlet 'X1' on building 'House 3'

All heights over ridge

Quantity | Value |
---|---|

Parameter for solid fuel combustion. Nominal heat output: 15 kW | |

Additive term H_{Ü} (Table 1) | 0.40 m |

Outlet height above reference level H_{B} (Table 3) | 1.00 m |

Radius of exposure zone R (Table 3) | 15.00 m |

Outlet building | |

Required outlet height for outlet building H _{A1}=H_{S1}+H_{Ü} (Equation 4) | 0.40 m |

Upstream buildings | |

Highest recirculation zone from the upstream building 'House 5' H _{A2}=H_{S2}+H_{Ü} (Equation 19) | 1.75 m |

Required outlet height for undisturbed removal H _{A}=max(H_{A1},H_{A2)} (Figure 2)) | 1.75 m |

Exposure zone | |

No air intake in exposure zone R H _{E}=0 | |

Required outlet height for adequate dilution H _{E}=max(H_{E},H_{E1}) (Section 6.3.1.1) | -8.40 m |

Height of exhaust gas discharge systemH _{M}=max(H_{A},H_{E}) over the ridge | 1.8 m |

## Calculation for the exhaust gas discharge system 'X2'

### Details for Outlet building 'House 3' - Symmetric pitch roof α ≥ 20°

Quantity | Parameter | Value |
---|---|---|

Height of ground over origin of coordinates (Section 6.2.4, Figure 10) | Δh | 0.00 m |

Ridge height | H_{First} | 10.40 m |

Eaves height (Figure 4) | H_{Traufe} | 6.70 m |

Actual roof height (Figure 4, Section 6.2.1.2.2) | H_{Dach} | 3.70 m |

Width of half of the gable end opposite the outlet. For symmetric roof this will be b/2 else b | b_{Luv} | 5.65 m |

Horizontal distance between the center of the outlet cross-section and the ridge (Figure 4) | a | 5.65 m |

Roof pitch angle (Figure 4) | α | 33.22 ° |

Roof pitch correction (interpolated with table 2) | γ | 2.15 ° |

Factor for determining H_{2} (interpolated with table 2) | f | 0.66 |

Height of recirculation zone for distance a to ridge (Equation 1) | H_{1} | 3.40 m |

Maximum height of the recirculation zone (Equation 2) | H_{2} | 2.43 m |

Calculated height of exhaust gas discharge system over ridge (Equation 3) | H_{S1} | 2.43 m |

### Details for building 'House 1' - Symmetric pitch roof α ≥ 20°

Quantity | Parameter | Value |
---|---|---|

Height of ground over origin of coordinates (Section 6.2.4, Figure 10) | Δh | -2.10 m |

Ridge height | H_{First} | 11.50 m |

Eaves height (Figure 4) | H_{Traufe} | 7.50 m |

Actual roof height (Figure 4, Section 6.2.1.2.2) | H_{Dach} | 4.00 m |

Width of half of the gable end opposite the outlet. For symmetric roof this will be b/2 else b | b_{Luv} | 6.70 m |

Horizontal distance between the center of the outlet cross-section and the ridge (Figure 4) | a | 5.71 m |

Roof pitch angle (Figure 4) | α | 30.84 ° |

Roof pitch correction (interpolated with table 2) | γ | 0.56 ° |

Factor for determining H_{2} (interpolated with table 2) | f | 0.69 |

Height of recirculation zone for distance a to ridge (Equation 1) | H_{1} | 3.33 m |

Maximum height of the recirculation zone (Equation 2) | H_{2} | 2.76 m |

Calculated height of exhaust gas discharge system over ridge (Equation 3) | H_{S1} | 2.76 m |

Horizontal extend of the recirculation zone (Equation 15, Figure 8) | l_{RZ} | 21.61 m |

Effective length of an upstream building (Equation 16, Figure 8) | l_{eff} | 16.88 m |

Angle between the gable side of the upstream building and the line to exhaust gas discharge system (Section 6.2.2.1, Figure 8) | β | 77.79 ° |

Horizontal distance of the exhaust gas discharge system from the upstream building (Figure 8) | l_{A} | 17.83 m |

Height of the outlet required by the upstream buildings over the ridge of 'House 3' (Equation 17, Figure 8) | H_{S2} | -4.44 m |

### Details for building 'House 5' - Symmetric pitch roof α ≥ 20°

Quantity | Parameter | Value |
---|---|---|

Height of ground over origin of coordinates (Section 6.2.4, Figure 10) | Δh | 1.70 m |

Ridge height | H_{First} | 11.00 m |

Eaves height (Figure 4) | H_{Traufe} | 6.10 m |

Actual roof height (Figure 4, Section 6.2.1.2.2) | H_{Dach} | 4.90 m |

Width of half of the gable end opposite the outlet. For symmetric roof this will be b/2 else b | b_{Luv} | 7.80 m |

Horizontal distance between the center of the outlet cross-section and the ridge (Figure 4) | a | 1.47 m |

Roof pitch angle (Figure 4) | α | 32.14 ° |

Roof pitch correction (interpolated with table 2) | γ | 1.42 ° |

Factor for determining H_{2} (interpolated with table 2) | f | 0.67 |

Height of recirculation zone for distance a to ridge (Equation 1) | H_{1} | 0.87 m |

Maximum height of the recirculation zone (Equation 2) | H_{2} | 3.29 m |

Calculated height of exhaust gas discharge system over ridge (Equation 3) | H_{S1} | 0.87 m |

Horizontal extend of the recirculation zone (Equation 15, Figure 8) | l_{RZ} | 21.03 m |

Effective length of an upstream building (Equation 16, Figure 8) | l_{eff} | 16.53 m |

Angle between the gable side of the upstream building and the line to exhaust gas discharge system (Section 6.2.2.1, Figure 8) | β | 87.07 ° |

Horizontal distance of the exhaust gas discharge system from the upstream building (Figure 8) | l_{A} | 19.47 m |

Height of the outlet required by the upstream buildings over the ridge of 'House 3' (Equation 17, Figure 8) | H_{S2} | -3.30 m |

### Height of recirculation zones for the upstream buildings

at the outlet system 'X2' over ridge 'House 3'

Name of the building | Height of recirculation zone H_{S2} |
---|---|

House 1 | -4.44 m |

House 5 | -3.30 m |

### Calculation for the outlet 'X2' on building 'House 3'

All heights over ridge

Quantity | Value |
---|---|

Parameter for solid fuel combustion. Nominal heat output: 15 kW | |

Additive term H_{Ü} (Table 1) | 0.40 m |

Outlet height above reference level H_{B} (Table 3) | 1.00 m |

Radius of exposure zone R (Table 3) | 15.00 m |

Outlet building | |

Required outlet height for outlet building H _{A1}=H_{S1}+H_{Ü} (Equation 4) | 2.83 m |

Upstream buildings | |

Highest recirculation zone from the upstream building 'House 5' H _{A2}=H_{S2}+H_{Ü} (Equation 19) | -2.90 m |

Required outlet height for undisturbed removal H _{A}=max(H_{A1},H_{A2)} (Figure 2)) | 2.83 m |

Exposure zone | |

No air intake in exposure zone R H _{E}=0 | |

Required outlet height for adequate dilution H _{E}=max(H_{E},H_{E1}) (Section 6.3.1.1) | -8.40 m |

Height of exhaust gas discharge systemH _{M}=max(H_{A},H_{E}) over the ridge | 2.8 m |

## Calculation for the exhaust gas discharge system 'X3'

### Details for Outlet building 'House 3' - Symmetric pitch roof α ≥ 20°

Quantity | Parameter | Value |
---|---|---|

Height of ground over origin of coordinates (Section 6.2.4, Figure 10) | Δh | 0.00 m |

Ridge height | H_{First} | 10.40 m |

Eaves height (Figure 4) | H_{Traufe} | 6.70 m |

Actual roof height (Figure 4, Section 6.2.1.2.2) | H_{Dach} | 3.70 m |

Width of half of the gable end opposite the outlet. For symmetric roof this will be b/2 else b | b_{Luv} | 5.65 m |

Horizontal distance between the center of the outlet cross-section and the ridge (Figure 4) | a | 0.00 m |

Roof pitch angle (Figure 4) | α | 33.22 ° |

Roof pitch correction (interpolated with table 2) | γ | 2.15 ° |

Factor for determining H_{2} (interpolated with table 2) | f | 0.66 |

Height of recirculation zone for distance a to ridge (Equation 1) | H_{1} | 0.00 m |

Maximum height of the recirculation zone (Equation 2) | H_{2} | 2.43 m |

Calculated height of exhaust gas discharge system over ridge (Equation 3) | H_{S1} | 0.00 m |

### Details for building 'House 5' - Symmetric pitch roof α ≥ 20°

Quantity | Parameter | Value |
---|---|---|

Height of ground over origin of coordinates (Section 6.2.4, Figure 10) | Δh | 1.70 m |

Ridge height | H_{First} | 11.00 m |

Eaves height (Figure 4) | H_{Traufe} | 6.10 m |

Actual roof height (Figure 4, Section 6.2.1.2.2) | H_{Dach} | 4.90 m |

Width of half of the gable end opposite the outlet. For symmetric roof this will be b/2 else b | b_{Luv} | 7.80 m |

Horizontal distance between the center of the outlet cross-section and the ridge (Figure 4) | a | 1.78 m |

Roof pitch angle (Figure 4) | α | 32.14 ° |

Roof pitch correction (interpolated with table 2) | γ | 1.42 ° |

Factor for determining H_{2} (interpolated with table 2) | f | 0.67 |

Height of recirculation zone for distance a to ridge (Equation 1) | H_{1} | 1.06 m |

Maximum height of the recirculation zone (Equation 2) | H_{2} | 3.29 m |

Calculated height of exhaust gas discharge system over ridge (Equation 3) | H_{S1} | 1.06 m |

Horizontal extend of the recirculation zone (Equation 15, Figure 8) | l_{RZ} | 21.71 m |

Effective length of an upstream building (Equation 16, Figure 8) | l_{eff} | 17.28 m |

Angle between the gable side of the upstream building and the line to exhaust gas discharge system (Section 6.2.2.1, Figure 8) | β | 84.60 ° |

Horizontal distance of the exhaust gas discharge system from the upstream building (Figure 8) | l_{A} | 9.57 m |

Height of the outlet required by the upstream buildings over the ridge of 'House 3' (Equation 17, Figure 8) | H_{S2} | 4.13 m |

### Height of recirculation zones for the upstream buildings

at the outlet system 'X3' over ridge 'House 3'

Name of the building | Height of recirculation zone H_{S2} |
---|---|

House 5 | 4.13 m |

### Calculation for the outlet 'X3' on building 'House 3'

All heights over ridge

Quantity | Value |
---|---|

Parameter for solid fuel combustion. Nominal heat output: 15 kW | |

Additive term H_{Ü} (Table 1) | 0.40 m |

Outlet height above reference level H_{B} (Table 3) | 1.00 m |

Radius of exposure zone R (Table 3) | 15.00 m |

Outlet building | |

Required outlet height for outlet building H _{A1}=H_{S1}+H_{Ü} (Equation 4) | 0.40 m |

Upstream buildings | |

Highest recirculation zone from the upstream building 'House 5' H _{A2}=H_{S2}+H_{Ü} (Equation 19) | 4.53 m |

Required outlet height for undisturbed removal H _{A}=max(H_{A1},H_{A2)} (Figure 2)) | 4.53 m |

Exposure zone | |

Highest air intake in exposure zone R (Building 'House 5') H _{F} | -0.10 m |

Required outlet height for adequate dilution H _{E}=H_{F}+H_{B} | 0.90 m |

Height of exhaust gas discharge systemH _{M}=max(H_{A},H_{E}) over the ridge | 4.5 m |