JET 39 JET Volume 13 (2020) p.p. 39-49 Issue 4, December 2020 Type of article 1.01 www.fe.um.si/en/jet.html COST-BENEFIT ANALYSIS OF FROST PROTECTION METHODS ANALIZA STROŠKOV IN KORISTI METOD ZA ZAŠČITO PROTI POZEBI Matej Fike R , Mateja Fekonja 1 , Miha Smrekar 2 Keywords: Spring Frost, Frost Protection, Cost-benefit analysis, NPV Abstract Agricultural losses due to frost are high in various parts of the world, and in Slovenia, frost damage has frequently occurred in recent decades. Multiple methods for preventing frost damage exist and have been researched more or less extensively. Despite this, frost prevention measures are relatively sparsely used in Slovenia. This article aimed to review and compare active frost prevention techno- logy for a case study of a typical fruit farm in Slovenia, based on a cost-benefit analysis. Most of the active methods require either large capital investment or have a high annual cost. According to our analysis, burning wood, used in Slovenia to battle frost damage in orchards and vineyards, proved to be the most cost-effective method, which is probably why it remains in wide use. Povzetek Izgube kmetijskih pridelkov zaradi pozebe so velike po vsem svetu, v Sloveniji pa se škoda zaradi poze- be v zadnjih desetletjih pojavlja vse pogosteje. Znanih je veliko metod za preprečevanje škode zaradi pozebe, ki so že bolj ali manj raziskane. Kljub temu pa se ukrepi za preprečevanje škode v Sloveniji zelo redko uporabljajo. Cilj tega članka je bil izdelati pregled in primerjavo različnih aktivnih ukrepov proti pozebi, ki so primerni za tipično sadjarsko kmetijo v Sloveniji na podlagi analize stroškov in koristi. Ugotovili smo, da so aktivni ukrepi dobra naložba, če so uporabljeni. Večina aktivnih ukrepov zahteva R Corresponding author: doc. dr, Matej Fike, Faculty of Energy Technology, Hočevarjev trg 1, SI-8270 Krško, Tel.: +386 7 6202 228, E-mail address: matej.fike@um.si, 1 Faculty of Agriculture and Life Sciences, Pivola 10, 2311 Hoče 2 Faculty of Energy Technology, Hočevarjev trg 1, 8270 Krško 40 JET JET Vol. 13 (2020) Issue 4 Matej Fike, Mateja Fekonja, Miha Smrekar 2 Matej Fike, Mateja Fekonja, Miha Smrekar JET Vol. 13 (2020) Issue 4 ---------- ali visok začetni kapital ali pa imajo velike letne stroške. Kurjenje, ki ga v Sloveniji uporabljajo za boj proti pozebi v sadovnjakih in vinogradih, se je po naši analizi izkazalo kot najbolj stroškovno učinkovita metoda, kar je verjetno razlog, da je še vedno v široki uporabi. 1 INTRODUCTION Among other weather-related phenomena, frost damage is responsible for serious agriculture production losses. The Food and Agriculture Organization of the United Nations reports that more economic losses have been caused by the freezing of crops in the USA than by any other weather hazard, [1]. In Slovenia, the frequency of spring frost was higher in recent decades than previously recorded, [2]. Fields and orchards can be protected from the frost by passive and active methods. Passive techniques cannot completely prevent frost damage, but it is very important to implement them because they make it easier and more efficient to implement active methods, [3]. This study aimed to make a cost-benefit analysis and comparison of active frost prevention technology for a case study of a typical fruit farm in Slovenia. For this study, we assumed that all analysed active protection methods have the same effectiveness and have compared the investment value of specific methods, based on the defined criteria. We also analysed the cost- benefit of wood-burning, which is commonly used in Slovenia to prevent frost damage to vineyards and orchards. 2 DATA AND METHODS 2.1 Net present value A thorough financial analysis should be conducted before investing in frost protection. A sound investment should satisfy three criteria: it must be profitable, the cash flow must be financially feasible, and the risk must be compatible with the preferences and financial position of the investor. Economic analysis of frost protection is complicated by the nature of weather and the net benefits derived from adopting a particular frost protection technology. One may not be able to evaluate the financial risk of the adoption decision unless adequate (e.g., 20- to 50-year time series) minimum and maximum temperature data are available, [1]. As discussed in the introduction, there are different ways to protect crops against frost damage. We focused on solid fuel heaters, liquid fuel heaters, sprinklers, wind machines, helicopter rental, and wood burning in the analysis. We decided to create an analysis of the Net Present Value (NPV) for each protection method. With NPV, a project is measured according to its value rather than its costs. NPV assumes that money today is worth more than an equal amount of money tomorrow. Since the calculation is based on forecasted cash flows, a risk exists that the planned cash flows will not be reached, and thus must be considered, [4]. We took each specific protection measure, made an analysis of the major cost factors, and divided the costs into acquisition costs and variable costs, which can depend either on the frost frequency or on the total frost duration. The energy requirement for protecting the orchard 𝐸𝐸𝐸𝐸 𝑅𝑅𝑅𝑅 was set to be 140 𝑊𝑊𝑊𝑊 𝑚𝑚𝑚𝑚 − 2 . JET 41 Cost-benefit analysis of frost protection methods Cost-benefit analysis of frost protection methods 3 ---------- 2.2 Solid fuel heaters and burning wood analysis Orchard heaters are commonly used to prevent frost damage to fruit and fruit trees. Multiple types exist: pipeline, lazy flame, return stack, cone, solid fuel and liquid fuel. Solid fuel heaters usually only consist of solid briquettes, which are placed on the ground and ignited. Proper location of the heaters is essential for the uniformity of the radiant heat distributed among the trees [5]. The number of heaters required per hectare 𝑁𝑁𝑁𝑁 can be calculated using the following formulation from [1]: 𝑁𝑁𝑁𝑁 = 𝐸𝐸𝐸𝐸 𝑅𝑅𝑅𝑅 𝐸𝐸𝐸𝐸 𝑂𝑂𝑂𝑂 𝐹𝐹𝐹𝐹 𝐶𝐶𝐶𝐶 (3.6 ∙ 10 7 ) = 503 ℎ 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑒𝑒𝑒𝑒 ℎ 𝑒𝑒𝑒𝑒 (2.1) where N is the number of heaters required per unit of orchard area, 𝐸𝐸𝐸𝐸 𝑅𝑅𝑅𝑅 is the energy requirement [ 𝑊𝑊𝑊𝑊 𝑚𝑚𝑚𝑚 − 2 ], 𝐸𝐸𝐸𝐸 𝑂𝑂𝑂𝑂 the energy output per heater [ 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 − 1 ], 𝐹𝐹𝐹𝐹 𝐶𝐶𝐶𝐶 is the fuel consumption per heater per hour [ 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 ℎ − 1 ]. In our case, we used the following values: 𝐸𝐸𝐸𝐸 𝑂𝑂𝑂𝑂 = 33.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 − 1 , 𝐹𝐹𝐹𝐹 𝑐𝑐𝑐𝑐 = 0.3 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 ℎ − 1 . If we assume that 1 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 of solid fuel costs 𝑝𝑝𝑝𝑝 = €4.45/ 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 , and that every heater has a mass of 𝑀𝑀𝑀𝑀 𝑈𝑈𝑈𝑈 = 2.5 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 , we can calculate the total price of solid fuel heaters per hectare per hour using: 𝑃𝑃𝑃𝑃 = 𝑝𝑝𝑝𝑝 ∙ 𝐹𝐹𝐹𝐹 𝐶𝐶𝐶𝐶 ∙ 𝑁𝑁𝑁𝑁 𝑀𝑀𝑀𝑀 𝑈𝑈𝑈𝑈 ≅ 270 € ℎ (2.2) We also took into account the acquisition costs of equipment related to solid fuel heaters, namely an ignition torch, a frost alarm, a minimum thermometer, with a total cost of €240, and an approximate surveillance manhour cost, which was approximated at €10/ ℎ/ 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 with four people controlling the fires. The total variable cost per hour is €310/ ℎ 𝑎𝑎𝑎𝑎 / ℎ. Additional costs are the labour costs of placing, starting, and stopping the fires, removal of waste, lighting torch fuel, etc., which were approximated to be €70/ ℎ 𝑎𝑎𝑎𝑎 per every frost event. For comparison, we calculated the same parameters for another solid fuel type, wood, which is commonly used to minimize frost effects in Slovenia. In this case, we assumed that 𝐸𝐸𝐸𝐸 𝑂𝑂𝑂𝑂 = 16 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 − 1 , 𝐹𝐹𝐹𝐹 𝐶𝐶𝐶𝐶 = 5 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 ℎ − 1 . Based on the energy requirement, we calculated that we would need 63 bonfires per hectare, each weighing 𝑀𝑀𝑀𝑀 𝑈𝑈𝑈𝑈 = 10 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 . We assumed that the wood price is €60/ 𝑚𝑚𝑚𝑚 3 , which, calculated with an average mass density of 470 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 / 𝑚𝑚𝑚𝑚 3 , gives us a price of €0.1277/ 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 . This gives us, together with surveillance costs, a total variable cost of approximately €52/ ℎ 𝑎𝑎𝑎𝑎 / ℎ. Variable costs, including manhour labour to set up the fires, fuel for trucks, etc., were estimated to be around €200/ ℎ 𝑎𝑎𝑎𝑎 per event. 2.3 Liquid fuel heater analysis Liquid fuel heaters typically burn up to 4 litres of fuel per hour. The maximum heating effect for a well-adjusted stand-alone heating system in the right environment is about 300 to 330 𝑊𝑊𝑊𝑊 𝑚𝑚𝑚𝑚 − 2 [6]. In our case study, we took into consideration liquid fuel heaters with the following data: Energy output 𝐸𝐸𝐸𝐸 𝑂𝑂𝑂𝑂 = 38 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑙𝑙𝑙𝑙 − 1 , fuel consumption 𝐹𝐹𝐹𝐹 𝐶𝐶𝐶𝐶 = 1.4 𝑙𝑙𝑙𝑙 ℎ − 1 . That gives us a total number of heaters per hectare of: 42 JET JET Vol. 13 (2020) Issue 4 Matej Fike, Mateja Fekonja, Miha Smrekar 4 Matej Fike, Mateja Fekonja, Miha Smrekar JET Vol. 13 (2020) Issue 4 ---------- 𝑁𝑁𝑁𝑁 = 𝐸𝐸𝐸𝐸 𝑅𝑅𝑅𝑅 𝐸𝐸𝐸𝐸 𝑂𝑂𝑂𝑂 𝐹𝐹𝐹𝐹 𝐶𝐶𝐶𝐶 (3.6 ∙ 10 7 ) = 98 ℎ 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑒𝑒𝑒𝑒 ℎ 𝑒𝑒𝑒𝑒 (2.3) Liquid fuel is typically burnt in some type of a metal container with an opening at the top. Among the initial capital costs required to invest in a liquid fuel heating system are the cost of heaters themselves, a fuel can, a fuel pump, a reserve tank, ignition torches, a frost alarm and a minimum thermometer. Altogether, we estimated the initial capital costs of the equipment to be €5,000. Variable costs per hectare include labour costs for starting and stopping the fires, refilling the heaters, and fuel for torches. Variable costs per hectare per frosting event were estimated to be €28/ ℎ 𝑎𝑎𝑎𝑎 . The total cost of fuel and labour of surveillance per hour was calculated to be €58/ ℎ 𝑎𝑎𝑎𝑎 / ℎ. 2.4 Sprinkler analysis Sprinklers can be used to provide sufficient heat to plants in an environment with little wind and appropriate temperatures, as long as a film of free-liquid water surrounds the fruit leaf. The required application can be estimated if heat loss by convection, radiation and evaporation is known, [7]. Among the initial capital costs are the main and secondary flow lines, tubing accessories, sprinkler heads, regulators, and trenching costs, the cost of the pumping plant, installation of the system, alarms and thermometers. Altogether, the equipment cost estimation was €7,450/ ℎ 𝑎𝑎𝑎𝑎 . Variable costs per hectare per frosting event, which included only the starting and stopping manhour labour, were valued at €11/ ℎ 𝑎𝑎𝑎𝑎 , while the variable costs per hour of protection were presumed to be €24/ ℎ. 2.5 Wind machine analysis Wind machines are tall, fixed-in-place, engine-driven fans that pull warm air down from high above ground during temperature inversions, and raise air temperatures in an orchard. They are not meant to be operated in windy conditions because high wind forces might cause too much stress on their blades, [8]. They are usually powered by internal combustion engines, although electrically powered fans can be used as well. Each wind machine, typically rated at 100 𝑘𝑘𝑘𝑘 𝑊𝑊𝑊𝑊 , is able to protect an area of around 4-5 hectares. In our analysis, a wind machine with an internal combustion engine was considered. The total acquisition costs of a single unit were estimated to be €35,000. Variable costs per single event per hectare, which include maintenance labour, vehicle use, and other miscellaneous replacement parts totalled €320.40/ ℎ 𝑎𝑎𝑎𝑎 per event. Variable costs per hour of protection, which include fan fuel cost and surveillance labour manhours were calculated at €19/ ℎ. JET 43 Cost-benefit analysis of frost protection methods Cost-benefit analysis of frost protection methods 5 ---------- 2.6 Helicopter analysis Helicopters have proven to be an effective method of crop protection. Bates, [9], for example, found the helicopter action could raise the crop temperature above the plant’s frost danger point. The affected area radius is approximately 𝑝𝑝𝑝𝑝 = 30 𝑚𝑚𝑚𝑚 , and 15- to 20-minute passes over the orchard are needed, [9]. We assumed in our case, that the investor will not buy a helicopter, but will rent one when needed. In this case, the only variable cost is helicopter and pilot rental per hour, which was estimated to be €1000 per hour. If we take into account an average helicopter speed of 15 𝑚𝑚𝑚𝑚𝑝𝑝𝑝𝑝 ℎ ( 𝑣𝑣𝑣𝑣 = 6.7 𝑚𝑚𝑚𝑚 / 𝑝𝑝𝑝𝑝 ), and the required pass-by time 𝑡𝑡𝑡𝑡 = 15 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑝𝑝𝑝𝑝 , we can approximately calculate the maximum area a single helicopter can cover within the given time span, given the width 𝑤𝑤𝑤𝑤 = 2 𝑝𝑝𝑝𝑝 = 60 𝑚𝑚𝑚𝑚 , that denotes the affected span of each pass by: 𝐴𝐴𝐴𝐴 𝑚𝑚𝑚𝑚 𝑒𝑒𝑒𝑒 𝑚𝑚𝑚𝑚 = 𝑣𝑣𝑣𝑣 𝑡𝑡𝑡𝑡 𝑤𝑤𝑤𝑤 = 6.7 𝑚𝑚𝑚𝑚 𝑒𝑒𝑒𝑒 ∙ 15 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑝𝑝𝑝𝑝 ∙ 60 ∙ 𝑒𝑒𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚 ∙ 60 𝑚𝑚𝑚𝑚 = 316,800 𝑚𝑚𝑚𝑚 2 = 31.68 ℎ 𝑎𝑎𝑎𝑎 (2.4) 2.7 Case study definition Our case study orchard farm is located in Slovenia. Based on model calculations made by the Agricultural Institute of Slovenia, available in [10], we estimated some typical values for a farm in Slovenia. Our chosen orchard area is 5 hectares. Annual fruit production mass is 40 𝑡𝑡𝑡𝑡𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 ℎ 𝑝𝑝𝑝𝑝 𝑒𝑒𝑒𝑒 𝑡𝑡𝑡𝑡 𝑎𝑎𝑎𝑎𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 . The selling price of apples is €0.49 / 𝑘𝑘𝑘𝑘 𝑔𝑔𝑔𝑔 , and the production costs add up to a total of €17,423 / ℎ 𝑎𝑎𝑎𝑎 . Based on available and gathered data, we estimated that one major frost event happens every two years, and the length of the frost is approximately 8 hours. During the frost events, damage occurs to the plants, affecting 50% of the fruit. The complete input parameters for our analysis can be seen in Table 1 and Table 2. 44 JET JET Vol. 13 (2020) Issue 4 Matej Fike, Mateja Fekonja, Miha Smrekar 6 Matej Fike, Mateja Fekonja, Miha Smrekar JET Vol. 13 (2020) Issue 4 ---------- Table 1: Input parameters to the cost-benefit analysis Input parameters Orchard area 5 ha Fruit mass 40 t/ha Crop price €0.49/kg Production costs €17,423 /ha Frosty year occurrence (x years) 2 years Number of frosts per frosty year 1 / year Length of every frost event 8 h Crop survival ratio 50 % Discount rate 4.00 % Project lifetime (years) 6 years Annual results, without frost Income per hectare €19,640/ha Costs per hectare €17,423/ha Profit per hectare €2,217/ha Total profit €11,087 Annual results, with frost Income per hectare €9,820/ha Costs per hectare €17,423/ha Profit per hectare -€7,603/ha Potential income per hectare €9,820/ha Table 2: Annual cost and investment data for each protection method Protection method Annual cost Investment Solid fuel heaters €12,750 €1,200 Liquid fuel heaters €2,460 €25,000 Sprinklers €1,015 €37,250 Wind machines €2,362 €35,000 Helicopters €8,000 / Wood burning €4,680 €1,200 JET 45 Cost-benefit analysis of frost protection methods Cost-benefit analysis of frost protection methods 7 ---------- The net present value (NPV) method requires three parameters for each period for which we wish to calculate the current investment value; the annual cash flow, the discount rate and the expected lifetime of the project, in which we want to yield positive results, minus the initial investment cost. The NPV formula can be written as: 𝑁𝑁𝑁𝑁 𝑃𝑃𝑃𝑃 𝑁𝑁𝑁𝑁 = ∑ 𝑅𝑅𝑅𝑅 𝑖𝑖𝑖𝑖 ( 1 + 𝑒𝑒𝑒𝑒 ) 𝑖𝑖𝑖𝑖 𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚 = 1 − 𝐼𝐼𝐼𝐼 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚 𝑝𝑝𝑝𝑝 𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 (2.5) where 𝑅𝑅𝑅𝑅 𝑚𝑚𝑚𝑚 is the estimated net cash flow for i-th period, 𝑝𝑝𝑝𝑝 is the discount rate, and 𝑝𝑝𝑝𝑝 is the life of the project. The initial investment in our case are all the costs of any equipment that have to be made before the first frost event occurs: the total equipment acquisition costs. We have chosen the net cash flow 𝑅𝑅𝑅𝑅 𝑚𝑚𝑚𝑚 to be the potential savings from protection, if a protection measure was to be installed or chosen to be used for protecting the crops. The effectiveness of all of the above measures was set to be 100 % to ensure the most optimal economic outcome in the case of investing. The results of the cost-benefit analysis can be seen in Table 3 and Figure 1. Our project lifetime is 𝑝𝑝𝑝𝑝 = 6 𝑦𝑦𝑦𝑦 𝑚𝑚𝑚𝑚 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑚𝑚𝑚𝑚 . 3 RESULTS Our economic analysis shows, as seen in Table 3, that all methods of protection yield effective results in the given project lifetime. Sprinklers, wind machines, and liquid fuel heaters require a large capital investment and have lower variable costs, while solid fuel heaters, helicopters and wood-burning require little to no capital investment, but have more significant variable costs. The most cost-effective method, according to our calculation, was burning wood, as it has the largest net present value of €105,003.64 after the designated project lifetime. The cost of all of the methods without frost events was considered to be zero, as little to no maintenance was considered to be required for the appropriate installed systems due to the short project lifetime. Table 3: Net present value of different active protection methods Protection method Annual cash flow (with frost) Annual cash flow (no frost) NPV (6 years) Solid fuel heaters €36,350 €0,00 €61,870.10 Liquid fuel heaters €46,640 €0,00 €93,069.37 Sprinklers €48,085 €0,00 €88,542.78 Wind machines €46,738 €0,00 €83,593.17 Helicopters €41,100 €0,00 €88,458.49 Wood burning €44,420 €0,00 €105,003.64 46 JET JET Vol. 13 (2020) Issue 4 Matej Fike, Mateja Fekonja, Miha Smrekar 8 Matej Fike, Mateja Fekonja, Miha Smrekar JET Vol. 13 (2020) Issue 4 ---------- Below, in Figure 1, the NPV of the protection methods is shown. It is clear that most of the protection methods give positive cost-benefit results (in this case, the NPV value is greater than zero for all analysed protection methods in just one year) after the initial capital investment, if calculating using the specified input data. Figure 1: Net Present Value of various active frost protection methods In Figure 2, we directly compare the total annual costs per hectare for our case study farm to illustrate the comparative cost of each protection method. Based on our calculation, a minimum of € 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐/𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉 of variable costs are needed to ensure sprinkler frost damage protection. Most methods have an annual variable cost range of approximately € 𝟐𝟐𝟐𝟐 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 /𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉 to € 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐/ 𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉 . Figure 2: Annual variable costs of various protection methods per protected hectare per frosty year The total investment costs per hectare are shown in Figure 3. Initial capital costs for renting a helicopter, wood-burning and solid fuel heaters are low while liquid fuel heaters, sprinklers and wind machines investment cost are high. -50.000 € 0 € 50.000 € 100.000 € 150.000 € 0 1 2 3 4 5 6 NPV [€] Time [years] Solid Fuel Heaters Liquid Fuel Heaters Sprinklers Wind Machine Helicopter Wood burning 0 € 500 € 1.000 € 1.500 € 2.000 € 2.500 € 3.000 € 2550 € 492 € 203 € 472 € 1600 € 936 € JET 47 Cost-benefit analysis of frost protection methods Cost-benefit analysis of frost protection methods 9 ---------- Figure 3: Investment costs of various protection methods per hectare 4 CONCLUSION Based on the conducted cost-benefit analysis, it is evident that frost protection systems, when effective, are beneficial in increasing the total profit of fruit producers, in an environment where frost is a relatively frequent occurrence. In our case study, all of the methods yielded positive economic results as soon as the first frosty year. The most effective measure was burning wood, which increased the potential profit (over the project lifetime of six years) by more than €100,000 in total. Sprinklers and liquid fuel heaters were approximately equally economically successful. Wind machines, helicopters, and solid fuel heaters have the smallest benefit-to-cost ratio, but these investments also gave positive investment value and are to be considered for potentially decreasing damage due to frost. 0 € 1.000 € 2.000 € 3.000 € 4.000 € 5.000 € 6.000 € 7.000 € 8.000 € 240 € 5000 € 7450 € 7000 € 0 € 240 € 48 JET JET Vol. 13 (2020) Issue 4 Matej Fike, Mateja Fekonja, Miha Smrekar 10 Matej Fike, Mateja Fekonja, Miha Smrekar JET Vol. 13 (2020) Issue 4 ---------- Figure 4: Example of burning wood in Slovenia References [1] R. Snyder, J. Abreu and S. Matulich: Frost Protection: fundamentals, practice and economics, Food and Agriculture Organization of the United Nations, 2005 [2] I. Kodrič, M. Lukačič and J. Prošek: Zaščita pred spomladansko pozebo, Ministry of Agriculture, Forestry and Food of Slovenia, 2006 [3] A. Soršak, Z. Kobal, I. Kodrič and D. Koron, Tehnološka navodila za zaščito pred spomladansko pozebo [Online], 2018. Available: https://www.kgzs.si/uploads/dokumenti/strokovna_gradiva/tehnoloska_navodila_za_z ascito_pred_spomladansko_pozebo_v_sadjarstvu_2018.pdf (31.12.2020) [4] S. Behringer: The Development of the Net Present Value (NPV) rule, Review of Economics & Finance, vol. 6, August, pp. 74-87, 2015 [5] U.S. Environmental Protection Agency: Orchard Heaters, AP 42, vol. 1, 5th ed., 1995 JET 49 Cost-benefit analysis of frost protection methods Cost-benefit analysis of frost protection methods 11 ---------- [6] R.G. Evans and A.S. Alshami: Pulse Jet Orchard Heater System Development: Part I. Design, Construction, and Optimization, Transactions of the ASABE, vol. 52, no. 2, p. 331, 2009 [7] J. Wolfe: Sprinkling for Frost Protection, Agricultural Experiment Station, Orgeon State University, 1969 [8] H. Fraser: Wind Machines for Minimizing Cold Injury (Infosheet), Ministry of Agriculture, Food and Rural Affairs, Ontario, 2008 [9] E. Bates: Temperature inversion and freeze protection by wind machine, Agricultural Meteorology, vol. 9, pp. 335-346, 1971 [10] Agricultural Institute of Slovenia: Model calculations for standard yield crops [Online], 2020. Available: https://www.kis.si/Standardni_nabor_1/ (30.12.2020) Nomenclature (Symbols) (Symbol meaning) t time N heater count per hectare 𝑬𝑬𝑬𝑬 𝑹𝑹𝑹𝑹 frost protection energy requirement 𝑬𝑬𝑬𝑬 𝑶𝑶𝑶𝑶 frost protection energy output 𝑭𝑭𝑭𝑭 𝑪𝑪𝑪𝑪 fuel consumption p fuel price P heater price 𝑴𝑴𝑴𝑴 𝑼𝑼𝑼𝑼 heater mass w helicopter affected protection width v speed A area NPV Net Present Value 𝑹𝑹𝑹𝑹 𝒊𝒊𝒊𝒊 net cash flow i annual period r required rate of return Cost-benefit analysis of frost protection methods 11 ---------- [6] R.G. Evans and A.S. Alshami: Pulse Jet Orchard Heater System Development: Part I. Design, Construction, and Optimization, Transactions of the ASABE, vol. 52, no. 2, p. 331, 2009 [7] J. Wolfe: Sprinkling for Frost Protection, Agricultural Experiment Station, Orgeon State University, 1969 [8] H. Fraser: Wind Machines for Minimizing Cold Injury (Infosheet), Ministry of Agriculture, Food and Rural Affairs, Ontario, 2008 [9] E. Bates: Temperature inversion and freeze protection by wind machine, Agricultural Meteorology, vol. 9, pp. 335-346, 1971 [10] Agricultural Institute of Slovenia: Model calculations for standard yield crops [Online], 2020. Available: https://www.kis.si/Standardni_nabor_1/ (30.12.2020) Nomenclature (Symbols) (Symbol meaning) t time N heater count per hectare 𝑬𝑬𝑬𝑬 𝑹𝑹𝑹𝑹 frost protection energy requirement 𝑬𝑬𝑬𝑬 𝑶𝑶𝑶𝑶 frost protection energy output 𝑭𝑭𝑭𝑭 𝑪𝑪𝑪𝑪 fuel consumption p fuel price P heater price 𝑴𝑴𝑴𝑴 𝑼𝑼𝑼𝑼 heater mass w helicopter affected protection width v speed A area NPV Net Present Value 𝑹𝑹𝑹𝑹 𝒊𝒊𝒊𝒊 net cash flow i annual period r required rate of return