How many people ratified the US Constitution in 1788?

Question

My great grandfather A. Woods was one thats why I'm asking.

Answer 1

Summary -- 1071 state delegates voted to ratify the Constitution when voting in their state conventions from 1787-1790.

[I also found your ancestor's name --see the final section of this answer]
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Clearly you are asking is about how many individuals voted for ratification of the Constitution at their state conventions, not about the vote for the document at the Constitutional Convention of 1787 (the latter would not be a "ratification vote" anyway).

The only thing I find slightly confusing about your question is that you ONLY list the year 1788, when in fact of the 13 original states only SEVEN of them ratified it during that year. The ratification breakdown by year was:

1787 - 4 states (DE, PA, NJ, GA)
1788 - 7 states (CT, MA, MD, SC, NH, VA, NY)
1789 - one (North Carolina)
1790 - one (Rhode Island)

I assume you want the total of ALL the delegates at these conventions who voted to ratify the Constitution, the total seems to be 1071

The following page charts most of the info, though it omits the totals for the three that voted unanimously (DE, NJ, GA), and contains a couple of errors (the only "aye" vote error is for PA -- see below).
http://www.barefootsworld.net/constit9.html

This link includes several total (though incorrectly listing the ayes in PA as 42; there were 46)
several totals given here, though it lists PA ayes as 42
http://www.sparknotes.com/history/american/constitution/htimeline.html

see also "The Six Stages of the Ratifying Conventions" by Gordon Lloyd
http://www.teachingamericanhistory.org/ratification/stages.html

As for your "1788" question -- if you for some reason ONLY want to know about the year, the "ayes" for that year totaled 703.
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As for your great grandfather (sure its not more generations than that?) -- you must mean Archibald Woods. You may well know this, but just in case you don't, or haven't seen the actual text of the document -- his name is included in the following ratification document from the VIRGINIA state convention (under the "ayes" list, of course)
http://www.constitution.org/rc/rat_va_23.htm

Answer 2

The signatories of the United States Constitution were the 39 delegates at the Constitutional Convention, led by George Washington, who signed the United States Constitution on September 17, 1787 in Philadelphia, Pennsylvania. No delegate from Rhode Island signed the document, since the state declined to send a representative. In addition, several notable politicians of the time did not attend the convention, including Thomas Jefferson and John Adams (both of whom were overseas working as diplomats), as well as Samuel Adams, Thomas Paine, and Patrick Henry (who considered the previous system of government acceptable). In addition to the signatories, a secretary by the name of William Jackson signed the document, not as a delegate, but in attestation of the document's signing.

Order Name Sending State
1George WashingtonVirginia
2George ReadDelaware
3Gunning Bedford, Jr.Delaware
4John Dickinson³Delaware
5Richard BassettDelaware
6Jacob BroomDelaware
7James McHenryMaryland
8Daniel of St. Thomas JeniferMaryland
9Daniel Carroll³Maryland
10John BlairVirginia
11James Madison Jr.Virginia
12William BlountNorth Carolina
13Richard Dobbs SpaightNorth Carolina
14Hugh WilliamsonNorth Carolina
15John RutledgeSouth Carolina
16Charles Cotesworth PinckneySouth Carolina
17Charles PinckneySouth Carolina
18Pierce ButlerSouth Carolina
19William FewGeorgia
20Abraham BaldwinGeorgia
21John LangdonNew Hampshire
22Nicholas GilmanNew Hampshire
23Nathaniel GorhamMassachusetts
24Rufus KingMassachusetts
25William Samuel JohnsonConnecticut
26Roger Sherman¹Connecticut
27Alexander HamiltonNew York
28William LivingstonNew Jersey
29David BrearleyNew Jersey
30William PatersonNew Jersey
31Jonathan DaytonNew Jersey
32Benjamin FranklinPennsylvania
33Thomas MifflinPennsylvania
34Robert Morris²Pennsylvania
35George ClymerPennsylvania
36Thomas FitzsimonsPennsylvania
37Jared IngersollPennsylvania
38James WilsonPennsylvania
39Gouverneur MorrisPennsylvania

Hmm, don't see him listed. Are you sure? Besides, if it's your great grandfather, you'd have to be pretty darn old and from a line of pretty darn old forebears.