Low-density foam is applied as low or high-pressure, two-component polyurethane spray foam. Low-density spray foam can be applied on walls, in unvented attics, to ducts and ceilings, and in vented attics and crawl spaces. It is known as an air barrier, but permeable to vapor and moisture. It is often used to fill cavities in walls during construction. http://youtube.com/watch?v=ggLAUsiuI_o&app=desktop

Spray foam insulation or spray polyurethane foam (SPF) is an alternative to traditional building insulation such as fiberglass. A two-component mixture composed of isocyanate and polyol resin comes together at the tip of a gun, and forms an expanding foam that is sprayed onto roof tiles, concrete slabs, into wall cavities, or through holes drilled in into a cavity of a finished wall. https://youtube.com/embed/ggLAUsiuI_o
Due to its relatively large cell structure, low-density foam stays somewhat soft and flexible after curing. This increases the likelihood of its continuing to provide high insulation value even as the building settles and shifts over time. Low-density SPF provides heat insulation and seals airflow through cracks, joints and seams by filling the cavities. In addition, this foam can help absorb sound thanks to its soft texture and open-cell structure. 

Spray Foam Attic Insulation

Medium-density foam is applied as low or high-pressure two-component polyurethane spray foam. Medium-density foam offers specific benefits depending on the climate and the type of building in which it is used. Like low-density foam, medium-density SPF is often used for continuous insulation, interior wall cavity fill, and unvented attic applications. However, medium-density is a closed-cell spray foam; it is often used where there is need for the greatest R-value insulation per inch possible. Medium-density foam acts as an air, vapor, and water barrier, and can even help reduce noise.
Apply coating when the roof is dry and the sealant has set. You will be using a 9-inch heavy-duty frame, ½-inch paint roller for spreading coating on roof or 1-1/4-inch roller for dipping in pail, and a 5–to-6-foot extension pole. Use a 3/4-inch roller with basecoats and emulsions. Map out your roof and make each pail fill that area. See Elastek Product Sheets for recommended coverage. An inexpensive 3-inch or 4-inch brush should be used to reach areas not possible with a roller. Use a stiff paintbrush for applying 103 Crack & Joint Sealant.
The guys who sprayed my attic were trained and certified, but I later found out, too late, that they had no experience and my attic was the first they'd ever sprayed. I was also never told to vacate my house for any length of time, and so I (and my pets) were in the house the day they sprayed and the entire time the off ratio foam was filling my home with horrendous vapors. The company kept telling me that it was a good job and I had nothing to worry about, even after I'd had 2 other experienced sprayers from 2 different companies visually examine the foam and confirm that large areas appeared to be off ratio. The 3rd sprayer from yet another company, was also outraged because the company who did my attic had failed to vacuum up all of the old cellulose insulation, and he also noticed areas where the foam was shrinking or pulling away, and this was not even 5 weeks after the spraying.  
We have a 1950's ranch in Atlanta and are interviewing foam contractors to spray open cell under the roof, with an "ankle wall" out towards the eaves to seal the attic. My wife and daughters are chemically sensitive, so I'm trying to figure out how to minimize the fumes coming into the house. Additionally, at least one contractor has offered (for > $900) to remove our existing rock wool & R-13 fibreglass from the attic floor to "increase cross-ventilation into the attic". Seems to me I can't both minimize fumes AND increase cross-ventilation. They also offered to spray a fire-retardant on for >$600. Would ventilation during installation help any or woud the retardant seal off the foam and help that way? Thanks...

Spray foam insulation works by sealing the building envelope to stop conditioned air from escaping and prevent unwanted outside air from entering your home. It allows efficient use of your HVAC system and helps regulate the temperature fluctuations and humidity in your home. It's a lightweight, durable, and versatile insulation solution boasting the industry’s strongest performance in energy efficiency and energy cost savings.

Also, I'm wondering... Is this website is being regularly updated? A local installer (in Oct, 2010) in MA quoted over twice the price you list here. "Open cell alone ~$1.35 per sq ft for R-13. Or a 'hybrid method' using 2inch closed cell for R-13 followed by 1.5inch open cell for R-6. Hybrid is $2.85 per sq foot for R-19 rating". Maybe installers are charging higher prices to profit from those trying to meet government energy rebate by Dec 31?

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We are turning our roof into an unvented roof assembly by raising the roof and blowing in SPF. We are planning to leave the existing vapor barrier down but remove the fiberglass batting and then adding 6" of SPF in all the cavities, to completely seal and insulate the house. Should we have any concerns about doing it "upside down" and not spraying the foam directly to the underside/sheathing of the roof?
Spray polyurethan foam does effectly prevent all six of these heat transfer methods from occurring. These should be the mechanisms by which you judge insulation, in addition to their R-Value. If you're uncertain about installing spray foam insulation, Energy Star has a map that recommends levels of insulation by R-value and cost-effectiveness in the United States.
If you cut the nails holding one of the corner studs to the bottom plate and the top plate with a Sawzall, you can use a flat bar (or a flat bar plus a wrecking bar) to pull the stud off the sheathing nails. Either re-use the stud, or buy a new stud, and install the stud with toenails as shown in the link I provided in Comment #51 (this link: Outside corner detail). https://www.youtube.com/watch?v=ggLAUsiuI_o&app=mobile

Jennifer, I'm not an expert on the health effects of closed cell foam. A lot of people live in houses with closed cell foam and have no health problems from it, at least not short-term, acute problems. I do know of one person who had it removed from her crawl space because she was convinced it caused her dog to get sick, but I know only what she told me.  
These coatings contain various types of acrylic polymer, and are typically formulated to help extend the coating’s life and improve durability. Acrylic coatings are available in a number of colors but are most commonly used as white reflective coatings. Thanks to its durability and low cost, many contractors and facility managers believe this to be the best roof coating.
SPF insulation applied by professionals is usually described as either a high- or low-pressure foam and is available as either open- or closed-cell. Each type has advantages and disadvantages depending on the application requirements. The comparison chart below can be helpful in explaining or understanding which type of SPF insulation is best suited to a specific application. 

Although spray foam insulation has been in use since the 1940s, primarily for aircraft, for the past 30 years, continual product innovation has seen the increased adoption of spray foam insulation in residential and commercial construction. The rapid growth of sprayed foam insulation in building construction, thanks in part to its immediate and long-term benefits, has allowed the insulation material to sit confidently alongside traditional insulation types in providing thermal comfort for building occupants. https://m.youtube.com/v/ggLAUsiuI_o
According to the Department of Energy, an estimated 20 to 40 percent of a home’s utility bill could be going to waste from drafts and air leaks around openings. As temperatures cool and energy costs rise, the positive impact of energy efficiency on a building comes into focus. Air can enter and escape a structure through every gap, compromising the building envelope. Adding the right insulation and air-sealing will close these gaps, keeping interior spaces comfortable and reducing energy bills.  http://www.youtube.com/e/ggLAUsiuI_o
Although spray polyurethane foam has many advantages over other types of insulation, spray foam installation isn’t foolproof. Some builders have reported problems with sloppy foam insulation. For example, some installers have been known to begin spraying before the chemical components are up to temperature, which can affect component mixing and foam performance. When components are poorly mixed, or mixed in the wrong ratio or at the wrong temperature, cured foam has been known to shrink away from rafters or studs, leaving cracks. Some installers rush through their spraying, resulting in voids.
Here's a simpler, less expensive alternative: Cut some 2-inch-thick rigid-foam insulation and glue it to the subfloor between the joists or support it with nails driven partway into the joists. Then fill any gaps between the edges of the foam boards and the joists using the canned spray foam sold at home centers or hardware stores. An even easier option is to nail the foam panels against the bottom edge of the joists and seal the joints with canned foam, but you'll lose some headroom and access to any pipes and wires between the joists. As with spray-foam kits, protect yourself and the floor from the dripping globs of canned foam. A full face shield, gloves, and a hat would be a good start.

Before you decide on spray foam or another method of insulation, it's important to understand the superiority of spray foam compared to traditional materials. When compared to fiberglass batts, spray foam offers nearly double the R-value per inch, achieves air-sealing and insulation in one step, won't be damaged by mold or moisture, and won't settle, compress, or otherwise be damaged to the point it needs replacement. https://www.youtube.com/watch?feature=youtube.be&v=ggLAUsiuI_o

I recently did a remodel project for my basement using spray foam insulation. The original builder has used fiberglass, but I wanted the best insulation i could find. We chose closed cell foam because it blocks moisture from getting into the house. It took one day to install and was fumey for about 3 hours. It was pretty cool watching it being done. It comes out as a liquid and then expands rapidly into a foam. It's quick! Then they took a types of saw to shave it flat with the wall studs so we could then go ahead and drywall.
R-value is the term given to thermal resistance to heat flow. The higher the R-value of an insulation product, the more effective the insulation properties. Spray polyurethane foam comes in a range of densities and cel structure. Low density foams are referred to as Open Cel SPF while higher density foams are referred to as Closed Cel foam. 1.8-2 pound polyurethane foam has the highest R-value of readily available spray foam insulation used in homes and buildings.[4]

Roof Spray Foam Insulation