# Benefits of Advanced Air Mobility for Society and Environment: A Case Study of Ohio
## 4 Benefit Factors
### BF-3: Cost and Delivery Time Savings in Package Delivery by Drones
#### 4.3.1 Cost Savings for Logistics Companies
Using Equation (12), we calculated \(N_{i}\) which denotes the normalized value of USA market size for drone package delivery in year \(i\) ($ million) relative to the value of \(U\) in year 2022:  
\[N_{i}=\frac{U_{i}*r^{\prime}}{U_{2022}}\qquad i\in\{2022,2023,...,2032(year)\} \tag{12}\]  
Then, the number of packages to be delivered or the number of annual drone delivery trips (as one drone can deliver one package at a time) in SMCO in year \(i\) (_pSMCO\({}_{i}\)_) was calculated using Equation (13), where _r\({}_{p_{i}}\)_ is the ratio of **P** and _P\({}_{US}\)_(see Section 4.2). As the value of \(a\) was given for year 2022, we calculated the normalized factor \(N_{i}\) to obtain _pSMCO_ (unit in billion):  
\[p_{SMCO_{i}}=N_{i}\times a\times r_{p_{i}}\qquad i\in\{2022,2023,...,2032(year)\} \tag{13}\]  
For estimating the number of working days of drone services in a year, we considered that Ohio averages 131 days of rainfall per year [51], and on a day with precipitation, there is a 61% chance of a thunderstorm or moderate rain [45]. Drones have trouble flying in moderate rain or thunderstorms; therefore, they are likely to face 81 (131 \(\times\) 0.61) days of flight delays or cancellations per year, leaving 284 uninterrupted operational days in a year. Package delivery drones, such as Amazon Prime Air delivery drones, have a maximum speed of 50 m per hour or 80.47 km per hour and maximum flight time of 30 min with 5 lb (or 2.268 kg) payload [45]. We considered 7.5 m (or 12.07 km) as the average flight radius (_d\({}_{2}\)_) for our analysis. Now, 50 m/ 1 h = 50 m/ 60 min = 7.5 m/ 9 min. As a result, this drone can deliver an item to 7.5 m distance and come back to station in 24 min (less than 30 min), which includes 6 min for flight acceleration and deceleration, package loading and unloading, and flight climb and descent. Thus, the maximum number of trips per year (_T\({}^{\prime}\)_) can be calculated Equation (14), where _R\({}_{t}\)_ denotes the round trip time (24 min):  
\[T^{\prime}=\frac{60}{R_{t}}\times 24\times 284 \tag{14}\]  
Now, _Y\({}_{i}\)_ is the number of delivery drones estimated to be in operation to deliver _pSMCO\({}_{i}\)_ packages in SMCO in year \(i\). At any given time, we assumed that another _Y\({}_{i}\)_ drones will be recharging. Then, _Y\({}_{i}\)_ can be calculated using Equation (15):  
\[Y_{i}=\frac{p_{SMCO_{i}}}{Tr^{\prime}}\qquad i\in\{2022,2023,...,2032(year)\}. \tag{15}\]  
Each station will require _Z\({}_{i}\)_ number of reserve drones in year \(i\) (assuming approximately 25% of drones in constant operation) to be ready on its busiest day, including backup for repairs or breakdowns to prevent running out of drones:  
\[Z_{i}=0.25\times Y_{i}\qquad i\in\{2022,2023,...,2032(year)\}. \tag{16}\]  
Thus, total number of drones is  
\[X_{i}=2Y_{i}+Z_{i}\qquad i\in\{2022,2023,...,2032(year)\}. \tag{17}\]  
For calculating the potential cost savings of logistics companies from using delivery drones, we compared the cost associated with the drone delivery system with the cost associated with the traditional delivery system using trucks, cars, or vans. We consider the following scenario: a logistics company like Amazon delivers its items to its customers through United Parcel Service (UPS). A UPS driver who delivers items for \(m=10\) h a day earns $25 per hour, and each day a driver can deliver up to \(n=250\) items. The delivery cost by truck (_q_) is around $30 per hour after factoring in petrol and tolls. It does not include Amazon's expenses of delivering items to UPS centers, gasoline, and other transportation costs, or any other contractual fees [45]. On the other hand, the capital cost of a drone used by Amazon is between $1000 to $3000 for the drone, $2000 for software and equipment, and the annual operating cost \(C_{o}\) (operator, maintenance, recharging, and other costs) is on average $800 [45]. We considered the average capital cost \(C_{c}\) is $4000 for each drone.