How much does it costs to transport 1 Ton of manure and/or compost on a per mile basis?

The cost of transport and application of solid or semi-solid manure and compost varies greatly within the different states and between countries. Custom haulers usually charge by load regardless of tonnage. A common practice is to charge by load up to one or two miles radius and from there charge on a per-mile basis.
When hauling solid stockpiled manure or semi-solid manure the moisture content will have a great variation between dairies according to their manure handling system, bedding material used, meteorological conditions, storage type, how long that manure has been stored, etc. In most cases trucks will be hauling a considerable amount of water.
When custom haulers or farm owners haul compost their major limiting factor is volume so haulers usually charge by cubic yard of compost regardless of tonnage.
Since fuel prices vary by time and location, the best way to put a dollar value to a manure spreading operation is to call local custom hauler companies and ask for a quote. Inquire about their trucks’ tonnage and volume capacities. Ask about their base price and distance and how much they charge for each extra mile. As an example, if a custom hauler charges $28 per load within a mile distance and their truck capacity is eleven tons, the cost will be 28/11= $2.54 per ton for the first mile. Extra miles may have different value (e.g. $2.0/mile). Those are real values for manure from one custom hauler in Southern Idaho as of June 2008.
eXtension “Cost of Manure Application and Transport” gives an idea on the factors related to solid and liquid manure transport and application.
The link “Contracting certified manure haulers” in that document offers an in-depth cost comparison between contracting custom haulers and using your own equipment.

What are typical values for the higher heating value of manure scraped from cattle feedyard surfaces?

The higher heating value of manure scraped from cattle feedyard surfaces depends primarily on its ash and moisture content. If the manure’s ash and water were completely removed with only the combustible fraction remaining as a residue, that (primarily organic) residue would have a higher heating value (HHV) of about 8,500 BTU per pound, as determined experimentally by Annamalai et al. (1987) and Rodriguez et al. (1998). That figure of 8,500 BTU/lb is known as a “dry, ash-free” (DAF) fuel value. To estimate the HHV of actual feedyard manure (i.e., in its “as-received” or “as-is” state), which always has some ash and some moisture in it, you can multiply the 8,500 BTU/lb figure by (1 – ash) and (1 – moisture). In this case, “ash” is the manure’s ash content expressed as a fraction (dry basis), and “moisture” is the manure’s moisture content as a fraction (wet basis). For example, a manure sample having 40% ash (dry basis) and 20% moisture (wet basis) would have an HHV of approximately: HHV(ash = 40%, moisture = 20%) = 8,500 BTU/lb x (1 – 0.40) x (1 – 0.20) = 8,500 x 0.6 x 0.8 = 4,080 BTU/lb Cattle manure (as excreted) has about 75% moisture and 15% ash, which translates to an HHV around 1,750 BTU/lb. On the feedyard surface, it generally dries out and may reach moisture contents as low as 15 to 20%. Depending on whether the corral surfaces are paved or native soil, the ash content may increase dramatically. HHV values between 2,000 and 5,000 BTU/lb are common, but they are highly variable because of moisture and ash dynamics of these outdoor facilities. Fuel value of manure generated in full confinement?under roof, on concrete?can be more tightly controlled.

Other cited literature:

Annamalai, K., J. M. Sweeten and S.C. Ramalingam. 1987. Estimation of gross heating values of biomass fuels. Transactions of the ASAE 30(4):1205-1208. Rodriguez, P.G., K. Annamalai, and J.M. Sweeten. 1988. The effect of drying on the heating value of biomass fuels. Transactions of the ASAE 41(4):1083-1087